The main problem is you have both Lulu and Janna (its overkill with the shields) and neither have much offence.
You lack damage as a result and you have over concentrated your damage into the Lux and Jinx.
Lux is pretty unreliable as far as damage goes because her Q is so volatile (in some games you get counterpicked, in other games they are too good and you can't hit your Qs).
I'd only run one of Janna/Lulu (you lose too much damage running both and neither can serve as a front line tank) and replace it with either a fighter tank (ex Darius, Renekton) who can bring some damage or a back up damage Mage top (ex Vladimir/Swain). Your comp becomes much more reliable and hard to deal with.