he definitely can, you just need to focus on what you need to do. The biggest thing about Lux is that if you can't get the pressure mid lane because it's a hard counter (fizz post 6, lb, etc), your main objective should be farming. If you go 0-0-0 in lane or even 0-1-0 in lane but you have a CS advantage, you will still average out and have the gold in order to build items to do damage. With that being said, definitely don't greed for farm. If you're missing a minion or two because they're pressuring you, just give it up because that ~36 gold is NOT worth giving the mid laner a kill and a chance to snowball. Just focus on what you need to do and remember that Lux is a good teamfight champion. She is able to do a possible LOT of AOE burst if you get a good E/R on a lot of them, or she is able to blow someone up with her combo, and she also has a utility shield/CC that really helps, even if she's a little behind. The biggest thing is to make sure you get that gold generation going through farming and possible kills/assists (it's pretty easy to get assists on Lux since you can R from far away to help out a fight or shield your allies for that juicy assist), and always do your best to kill or at least blow up/knock out a carry or two out of teamfights so you win teamfights and gain even more objectives and objectives.
In hard lanes, depending on who I'm against, I like to just farm up and try to put pressure on the map elsewhere if possible, like getting my ADC ahead bot lane or even scoring kills of my own bot or top in order to be more of a threat for the enemies. Just remember not to leave a lane to possibly help your teammates and lose 2+ waves, it's not worth it in the end.