I am Silver 3 and I played a lot of caitlyn with the normal items. I'm bored of it and I was looking at the attack speed run and thinking "Why do we always take this.. sure the dps is higher but what if I take the extra ad" so I took it and I played a game and it felt pretty good.
I then built a lethality item and I really loved the damage coming out of the EQ combo. I tried a bunch of builds and I have settled on Serrated dirk > Collector > IE > BT > Storm razer/LDR For boots I normally sit on tier 1 until IE is done.
I have gotten a lot of shit for this because its a crap build. But its working for me and I have tried peoples suggestions of going Yommu's > collector > sedge and it doesnt feel as good.
For runes I take fleet footwork, PoM, Alarcity, coup. Then AF and gathering storm.
For combo AA > E > Q > AA
lvl 2 damage with longsword is 462
lvl 5 damage with dirk is 712
lvl 9 damage with collector is 1286
Personally never been a fan of Lethality Caitlin, the traditional crit builds are better and scale better. BUT if you want to play Lethality I recommend looking up FSNx Saber, he plays A LOT of Caitlin and has lethality videos on his channel.