Hello and welcome, this is an attack speed ap lulu build, lulu is a very powerful ap carry she can deal very high amounts of damage from a big range!
Whimsyshrine is a reference to Whimsyshrine from diablo 3 where u find ponies, teddy bears and other kinds of cute things that actually are very overwhelming, appearance doesn't mean anything

attack speed magic penetration and ability power grant her give damaging power also armor to grant some survivability feel free to change the armor runes for magic resistance ones if u want

armor penetration and magic penetration will grant massive amount of power also some gold for bigger income and some mana regeneration

Boots:Boots of swiftness, Mercury's threads, Sorcerer's shoes
Base build:Lich bane+nashor's tooth+Boots+Rabadon's deathcap
End game items:Hextech gunblade, Nashor's tooth (2nd), Guinsoo's Rageblade

Q:2 seconds of 90% slowing and a good amount of magic damage max it by 9 lvls
W:grants 1 and a half blasting wand and some movement speed max by 13 and use it either for a damage burst or either for a good escape
E:Small shield u can use it to allies to save from ignite or bleed effects but sometimes its not enough also causes ur pix to to to that target from there u can fire ur Q for additional range make sure to use it on minions to to get high range at early lvls and not only max it 18
also deal damage to an enemy and reveals them
R:Grants massive amount of health boost plus knocks enemies around to the air very useful to escape or even to secure a kill

Flash grants her some escape power and i think it the best choice ghost is also good but she already to a speed boost also exhaust can be very good to secure a kill or escape
Ignite can be very overwhelming and useful and is the best choice although surge is also very powerful id suggest getting either surge or ignite and not both at the same time

Pros
Big escape power
Great cc
Easy to last hit kills
Very supportive

Cons
Not very high survivability skill
Mana drops very easily (early game only)

Thanks for checking this attack speed ap lulu build hope u enjoyed it :)
if u r interested u can also check my builds for ap karma, karma jungle, solo top mundo or blitzcrank support