Against caitlyn, Caitlyn has limited self peel outside of her t. Whenever she is overextended with her E on cooldown, you should look to take her down. If she is not using her E and is playing safe, you could try a Flash engage or ambush her from inside a bush.
 
An enemy Caitlyn can dish out a lot of damage in a team fight if she is left unchecked. Try to focus her down as soon as possible so she is unable to dish out lots of damage. If she is being protected, try to flank her.
 
Punishing Caitlyn in the early game will reduce her ability to snowball and destroy your tower. Try and set her behind by killing her over and over with assistance from your allies. Against caitlyn, If she doesn't use her E and plays safely, you can try a flash to engage her or lure her from inside a bush. An enemy Caitlyn can deposit a lot of damage in a team fight if she is left unchecked. Try to concentrate her as soon as possible so she is unable to deposit a lot of damage. If she is protected, try to surround her. Punishing Caitlyn in the early match will reduce her ability to snowball and destroy your turn. Try and place her behind by killing her again and again with the help of your allies.