League of Legends

Your build is absolutely fine and won't hinder you from winning games in silver elo.
After taking a look at your opgg, I would suggest focusing on improving your cs/m and minimizing deaths.

That being said, target dummy dps does not really tell the whole story.
In some games where you are against an armor-heavy enemy team, buying collector will delay the point where you can actually deal significant damage to the enemy frontline.
As for Infinity Edge, it certainly has its value, but in some games you might find that you need the extra mobility that galeforce provides since you will be dealing 0 dmg when dead or zoned.
Obviously, if you are not yet comfortable using galeforce then IE will be better in every game.

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.

Testing with the normal build the damage is less even if I add an extra auto to the end of the combo. It needs about 2-3 extra auto attacks to achieve the same damage. But by level 9 it seems attack speed does a lot more damage.

I feel like there is a way to make this build work but I am doing something wrong. https://www.op.gg/summoners/oce/Fizz%20Mortune

EQ Brother