If you're reading this you've seen the flashy title, and are curious to see how you can ever solo lane with Kalista. Some of you are yelling "what about the Ultimate and W passive?! She's clearly meant for a duo lane!" But if I may take some of your time, this build is very fun to play and very easily works out if done properly.

While Mid Kalista has the obvious advantage of the ability to dodge skillshots most mid-laners have, she can actually contribute a lot to teamfights in the late-game if you manage to win lane.

This build focuses on dealing damage, map presence (by being mobile), and being in the enemy's face constantly.

"Let's see how many spears you can endure!"
- Kalista, The Spear of Vengeance

The main idea behind this build is to constantly be in the enemy team's face. No matter what you decide to build (there's a number of options), you always have your Attack Speed mobility, which is perfect for Mid lane farming and pushing towers. And you can always have Vision on river with your Sentinel (W) from Mid.

If you play smart in the early game, you superior AD and AD scaling should be able to grab you a few kills in-lane, so you can grab all the expensive items I propose. Then once you grab a few health items (from the Core items) and are able to dodge CC, you can push lane to your heart's content. Be sure to get vision of river/jungle with your Sentinel (W) to avoid Ganks. After which you can roam and help your teamates.

Depending on the what you build, the late-game can go a few different ways. But for most of these ideas, you just jump around the enemy dealing fairly good damage. And because you have higher health, you can take quite a few hits before dying (at which point, you've slowed them with the Frozen Mallet and/or your Rend (E) and the carry cleans up)

While the Passive on your Sentinel (W) and Fate's Call (R) can't be used in-lane, they are incredibly useful in teamfights. While you can poke and force the enemy to engage or engage yourself, you can Ult your tank into the enemy, knocking them up (another way to engage). Or you can Ult your ADC if they're out of position and/or save them.

-Explaining the Core

Kalista as always revolves around Attack Speed, so getting that quickly is important. Her passive's range is based on your Boots' tier, so there is a strong argument to Rush Berserker's Greaves, but it depends on how aggressive your lane opponent is (dodging skillshots).

Your first two items should be Runaan's Hurricane and Black Cleaver (getting Tier Two Boots along the way). The idea is to saty in your enemy's face with your Range, Attack Speed, and Mobility. And BC is to be able to take a few hits before having to go back to base (Or simply be more agressive). The cooldown reduction from BC also gives you more chances to use Rend (E) to slow your enemies to set up kills or execute them.

Sometimes it's hard to tell when to use your Rend (E) to slow or execute your enemy when you're focused on chasing them with your passive, so you can get more time with Frozen Mallet's slow.
FM and BC along with your Runes and Masteries give you 3,000+ Health Late-Game, so the only way you can die really is to get Stunned (this also gives you the chance to peel for your ADC if needed).
Kalista doesn't need to get a lot of high damage items to still mow down out-of-place targets, so becoming bulky helps sustain and map presence.

There are many ways you can go from the core build. They're as follows (in order of usefulness):

(bare with me, I go into detail)

-Spellcaster:
If your team is lacking CC, Getting an Essence Reaver and Zephyr gives you 40% CDR, so you can activate your Rend (E) very often.
The ER is overkill to maintain your mana, but this way you don't need to worry about it at all. The main reason for ER is to get the damage spike, CDR and Lifesteal (which works well with your Attack Speed).
The Zephyr gives you the most mobility you'll have with Kalista. You'll have well over 400 Movement Speed with BC passive, so chasing Enemies is fairly easy (not to mention the Attack Speed boost). The Tenacity also makes it just a little more likely to escape a Stun.

-ADC:
ADC is a hard role to play. When bot lane has a distinct winner, someone is having a bad game getting yelled at. If you're ADC doesn't recover, you AD scaling makes it very easy to take over the role.
I recommend you Trade in your health items (Black Cleaver and Frozen Mallet), but there are situations you can get away with having them (just get Trinity Force and Infinity Edge if this is the case).
When getting rid of one or both of your health items, you can pick up either BloodThirster or Trinity. But getting both is good for sustain/durability ((Attack Speed/Health/Life Steal) Higher Critical Hit chance with IE).
When in doubt, get Blade of the Ruined King over Last Whisper for Attack Speed and Life Steal. But if the enemy has a lot of Armour, you obviously want Armour Penetration from Last Whisper.
If you've read this far, I don't need to explain why you need Infinity Edge. It's vital on any ADC.

Still with me? This Build is super Versatile. I just want to make sure you have all the information and my thought process here.

-Armour Penetration:
If you're not doing very well you can fall back on simply helping to set up kills for the carry, by ripping apart their armour. Keep the Core build and get a Last Whisper and choose between Blade of the Ruined King, or Youmuu's GhostBlade. The Armour Penetration from Black Cleaver and Last Whisper should be enough and you can simply get BoRK for Attack Speed and Life Steal (sustainability), But if they're tank is a wall like Volibear, Zac, Singed etc. some extra Armour Pen from GhostBlade couldn't hurt

-Mobile Tank?!:
You thought I was crazy to suggest Kalista go mid as an AD caster, so now I must be insane, right?! But hear me out. With the core build alone you have 3,000+ Health, and high mobily from your Attack Speed. But if You add other tank items, not only can you egage, you can deal fair Damage and Slow enemies with FM and Rend (E), and disengage.
Dead Man's is a must for Movement Speed/Health/Armour. If the enemy team has a lot of AD, grab a Thornmail to punish them for trying to focus you. It's also good for general survivability. If they have mixed damage, grab a Warmogs over Thornmail. And if they have an AP carry, grab a Banshee's to block abilities.

When I tried these ideas I couldn't decide if Kalista was broken or I was just facing really dumb players (very likely both). Regardless, Kalista is arguably the most mobile champion with the fewest items/abilities put into mobility. With this kind of mobility over your enemy and being able to deal constant Damage from autos, you can play around with a number of different ideas and make it work out. And if not you can easily have a large amount of vision if you grab a few wards and use your Sentinels (W).

I hope this build at the very least entertained you, and I wish you the best of luck on the feilds of justice, summoner!