I am talking about picking up morello earlier, you grabbing tear > mejais, delays that powerspike by too much.
I didn't say Lux has no late game, I said she isn't super late game. Yes her ult does a hefty chunk of damage and she brings utility, but compare her to some other champions that can bring more than her to the late game. Lux is very much so a midgame champion where damage and pick making with snares is unreal in a dragon fight or such.
"I upgrade trinket eventually" its 250 gold and increases your vision considerably OR you swap to sweepers to deny vision to increase your pick potential. There is no reason to not upgrade it as soon as you hit level 9 and have 250 gold available.
Lux doesn't have awful pushing power (granted her E's cost does need to be lower), and having the enemy beating on your mid tower all laning phase is bad because it makes it super easy to take at any opening. Once it falls it gives way too much lenience for the enemy team to roam/rotate. You need to push the lane up, and go make a play in top or bottom lane. Running teleport means you can get in an advantage position by tele'ing to a ward, or you can just walk down there and after you do your thing you can recall and then tele back to mid (or to an objective) to miss as little farm as possible.
I did notice you not getting many blue buffs either, you need to let your jungler know you need either the 2nd or 3rd blue if at all possible so that you can take advantage of your awesomeness without just going oom.
You did have a few bad top laners (how the hell was that one Jax a diamond player XD). But you not having boots means it is harder for you to get into position in time for team fights...grab some damn boots and get in range for your Q's and E's. I'd jump on someone not running boots and full damage too because they are going to die and it eliminates a pretty big threat.