Lillia in my opinion is a very fun champ thematically and gameplay-wise, ever since her release I've been wanting to bring that playstyle to the support role because I personally hate jungle as a role, and since the item rework happened, I've been trying my best to make it fun AND playable.

Prancing around the rift, placing wards, sleeping enemies, its really fun once you understand the basics!

Obviously she's also very cute, so that's a huge plus, no? :P

• Really good into tanky/slow comps, you get to proc item passives like Rylai's Crystal Scepter, Imperial Mandate or Demonic Embrace a lot and deal a considerable amount of damage with your Dream-Laden Bough and true damage.
  
  
• Since its an off meta build, you can use the lack of enemy knowledge in your favour.
  
  
• Your Lilting Lullaby is a really powerful teamfight tool, which can single handely win teamfights on later stages of the game.
  
  
• Spikes really hard and can win most 2v2s once you have Rylai's Crystal Scepter and Lilting Lullaby at hand.
  
  
• Scales pretty well and build is pretty flexible, you can use and combine tank, mage and enchanter items if needed.

• Aside from Swirlseed, your range is mostly limited, so you need to be good at trading with Blooming Blows in laning phase.
  
  
• Not the most noob-friendly pick, requires a bit of champ and range knowledge to be effective against competent players.
  
  
• Her mobility is fairly conditional, so fighting in the jungle is awkward at times if enemy is long-ranged or if there are no camps to stack Blooming Blows.
  
  
• Auto Attack range is low, so removing a Stealth Ward or Control Ward is dangerous if you don't have stacks/enough tankiness.

Whenever you hit someone with an ability, they get applied Dream-Laden Bough, it counts as a separate ability, so its extra gold for Spellthief's Edge, this passive deals 5% of the target's maximum hp over 3 seconds since lvl 1 with no ap, so its pretty good vs the likes of Nautilus or Braum, it also heals for 6 to 90 hp (based on level) + 30% of your AP which is also increased by heal power from items like Redemption and runes like Revitalize, that being said, early on you're better off hitting stuff like scuttle since the base healing for monsters is 39 (54 at lvl 18).

This ability has a range of 485 in the outer ring, for reference, Morgana has a Auto Attack range of 450, and so does Thresh, the outer ring also does true damage, so it oneshots Zyra's plants, with every ability you hit you get a prance stack, these stacks last 6.5 seconds and give you percent bonus movement speed, so its pretty good for roams.

Watch Out! Eep! is a dash that doesn't go through walls, but it can be pretty useful to dodge stuff or to run away when you're about to get rooted or are slowed, it also hits really hard, which means a good hit during a early 2v2 can turn around a fight with the sudden burst.

Cooldown is 14 seconds, and applies Dream-Laden Bough, which means you get double procs of Spellthief's Edge, the slow is also quite good during the early game, while also lasting 3 seconds, so its a good tool to enable ganks.

This ability takes 0.3 seconds to arrive no matter the distance so be mindful of that when you hit a long distance Swirlseed, the cooldown is high (150 to 110 seconds!), so make sure to hit at least 2 or more people to make it worth the use.

• When you're playing Lillia, the use of your passives is the key to success, since you get movement speed, apply slows, damage over time and so on, plus a decent amount of sustain from Dream-Laden Bough.
  
  
• Early game is all about taking safe trades and reaching your power spikes, which is mostly unlocking Lilting Lullaby and Rylai's Crystal Scepter, however don't think you can't win any 2v2s, people often disrespect the pick and a nicely aimed Watch Out! Eep! can turn the fight on your favour, plus Exhaust and Ghost can deny early kills if used properly.
  
  
• Melee matchups like Taric/ Braum/ Alistar allows you to bully them out of lane with ease, and Exhaust + Ghost should guarantee your survival.
  
  
• You dont have to hit Swirlseed directly, most botlaners tend to hide behind minions, but Lillia's Swirlseed does a cone splash once it hits anything (walls included), use this tactic when enemy adc steps up to farm.
  
  
• Whenever you hit a enemy champion with an ability, you'll proc Dream-Laden Bough, which will start healing you, it gets reduced to 33% if its more than 1 champion (so 100% + 33% healing).
  
  
• Remember that your Swirlseed keeps rolling until it hits something, so get creative, use it to facecheck a bush, throw it from river to river, from base to lane, and who knows, might hit someone with it, and since Lilting Lullaby has unlimited range, it can lead to a kill, it can also be used to mess someone's recall several times if you have vision of them and enough ability haste.
  
  
• You can heal off camps, so Q'ing Gromp , Scuttle or Rift Herald / Drake can give you a little bit of sustain when roaming.
  
  
• Since the build isn't AP heavy (at the start, at least), you can freely stack from a minion wave, Raptors or Scuttle as long as you hit them with the Inner circle of Blooming Blows.
  
  
• Blooming Blows has a very fast cast time, so a quick way to get 3 Spellthief's Edge procs is to Q and AA the enemy support when they try to reach the cannon minion for their Relic Shield proc.
  
  
• Lilting Lullaby is a proyectile, so be careful when dealing with Yasuo or Samira.

Lillia starts with Spellthief's Edge and the usual two Health Potion.

I used to suggest starting with Relic Shield, but after the 11.18 changes, Lillia's Swirlseed's cd got reduced and her Blooming Blows's stacks last a second longer, using Spellthief's Edge is more efficient, and besides, her base hp regen and hp regen growth got heavily reduced, so the extra hp regen from relic shield is minimal.

After first back you should aim for Giant's Belt, it'll make you deceptively tanky and win you some fights where you get engaged on, if you don't have enough gold at that point, you get a Ruby Crystal or Boots.

After getting enough gold, your Blasting Wand/ Giant's Belt turns into Rylai's Crystal Scepter, this, combined with your Lilting Lullaby is very strong in a 2v2 scenario.

For boots I generally get Ionian Boots of Lucidity since early Ability Haste is pretty good for Lillia, otherwise I go Mercury's Treads or Plated Steelcaps if needed.

There are a bunch of items you can get before or right after your mythic

• Stopwatch for early dive plays, or if enemy team has burst so you can survive after using Lilting Lullaby.
  
  
• Oblivion Orb if you're facing enemies with healing Yuumi/ Soraka/ Nami and you dont have Ignite for whatever reason.
  
  
• Dark Seal if you're in a easy matchup and are getting kills/assists often but dont want to commit to building full ap.

As for your mythic, your options are the following:

• Night Harvester (good amount of ability haste + hp and ap, useful if you cant afford to have long fights)
  
  
• Shurelya's Battlesong (mythic passive gives ability haste, which is good, and the active is pretty useful for a easier engage/disengage)
  
  
• Everfrost (extra layer of crowd control + mana and ability power)
  
  
• Jak'Sho, The Protean (insane synergy with your passive since Dream-Laden Bough keeps the item active for longer, combined with Conqueror you can frontline quite well, specially since Rylai's Crystal Scepter will keep everyone slowed)
  
  
• Radiant Virtue Very good for team-wide utility and tankiness, despite the nerfs its still a good item, it'll probably be optimal once the activation is manual (in future patches, hopefully) instead of needing to use Lilting Lullaby

Some of your other options are:

• Mikael's Blessing (HP, Heal power and a cleanse for stuff like Enchanted Crystal Arrow)
  
  
• Redemption (Raw heal power and a great active, plus HP)
  
  
• Warmog's Armor (VS poke heavy comps)
  
  
• Zhonya's Hourglass (Good for engage, if you want to flash in and use Lilting Lullaby)
  
  
• Randuin's Omen (Fed ADCs or stuff like Yasuo)
  
  
• Staff of Flowing Water (to boost both yourself and mages on your team, requires Font of Life)
  
  
• Spirit Visage (Magic Resist, HP and more self healing)
  
  
• Ardent Censer (If you have an Auto-Attack heavy team, requires Font of Life)
  
  
• Cosmic Drive (For Swirlseed spam and easy kiting combined with your slows)
  
  
• Chemtech Putrifier (Good against healing like Soraka's or items like Bloodthirster)
  
  
• Turbo Chemtank (Good mr item, also pretty good active for engages if you don't have Ghost available)
  
  
• Force of Nature (really good vs teams with a lot of cc and magic damage)
  
  
• Vigilant Wardstone (Quite cheap, good stats and a replacement for Shard of True Ice in very late game situations)
  
  
• Imperial Mandate (very good synergy with Rylai's Crystal Scepter, gives a decent amount of mana ability haste, AP and mana regen, which is neat if you're not using Presence of Mind)
  

(Or any mage items if your team needs magic damage)

When you're full build, I highly suggest to exchange your boots for another legendary item such as Dead Man's Plate since it gives you enough movement speed along with your Blooming Blows's passive and possibly Cosmic Drive.

Dark Harvest is an excelent rune for lillia, your Dream-Laden Bough procs it and provides kill pressure on botlane, its certainly useful when you pull a big ult and the resets help securing the kills.

Taste of Blood provides good sustain for laning phase, which is needed since you're a melee champion and are bound to take a decent amount of poke and you're mostly throwing Swirlseeds for poke and sustain through Dream-Laden Bough

My favourite rune for support, extra vision and ap, since you're often clearing wards its fairly easy to stack it safely.

Ultimate Hunter Very good rune since Lilting Lullaby has a fairly long cooldown until you stack Ability Haste and get some levels.

Lillia's Q ( Blooming Blows) mana cost is moderately high for how spammable it is, so having mana and hp sustain in case you're getting poked out is always good.

Having lower cooldown on items and on Flash/ Exhaust is extremely valuable, specially if you find yourself doing multi-man Lilting Lullaby when contesting objectives, which is why I choose Cosmic Insight.

Conqueror is the best rune to combine with Jak'Sho, The Protean, since you get extra damage and sustain, plus getting Legend: Tenacity from the smaller runes, it also got way stronger after Lillia became melee on patch 12.22.

Presence of Mind Gives a lot of mana, which is good since you'll be taking long fights, got better after Lillia became melee.

Legend: Tenacity is pretty much the best rune for Lillia, you don't need attack speed, and lifesteal is useless.

You're bound to soak in a lot of damage, the other runes aren't as effective, specially Cut Down since you'll often have very high amounts of hp, so Last Stand is the best choice.

Conditioning has great synergy with Jak'Sho, The Protean, but you may need Second Wind against some matchups.

Overgrowth gives hp, which means more tankiness, very good with the general build since Rylai's Crystal Scepter and such give tons of hp.

Guardian (and the whole resolve tree) is what keeps you relevant early game since the shield can keep your adc safe during trades where your abilities are on cooldown, and it can come in clutch overall for any situation (dives, close trades, etc etc).

Font of Life applies whenever you slow an enemy, either through a Swirlseed, Lilting Lullaby or with any ability if you have Rylai's Crystal Scepter, it is not the biggest heal in the world, but it adds up with all your other runes and items, it also procs stuff like Staff of Flowing Water.

The choice between Second Wind and Bone Plating is merely dependant on if the enemy botlane is poke focused or all-in focused, though personally I feel that Second Wind is overall better in every matchup, since a single Ashe Volley breaks Bone Plating and loses a lot of value.

Overgrowth: is most useful when you simply wanna be tanky and there isn't much cc to deal with. Revitalize: works best when combined with Dream-Laden Bough's self healing and items like Redemption. Unflinching: take it when facing stuff like Leona, Ashe, Nautilus and so on.

Lillia's Q ( Blooming Blows) mana cost is moderately high for how spammable it is, so having mana and hp sustain in case you're getting poked out is always good.

Having lower cooldown on items and on Flash/ Exhaust is extremely valuable, specially if you find yourself doing multi-man Lilting Lullaby when contesting objectives, which is why I choose Cosmic Insight.

For rune shards I like taking Ability Haste, Armor and HP, its quite a sizeable help in the early game since you're way tankier and you can throw Swirlseeds more often, only downside is that you clear Stealth Wards a bit slower.