Just one dude's advice, not saying this is gospel - - honestly just wait him out. Get whatever CS you can (probably not much) under tower, use your Q heal whenever appropriate, try not to take bad trades. Buy tabis early and maybe a cutlass for sustain, and keep your chin up.
Eventually you turn into a split pushing monster and you can just pressure whatever side lane he's not in. Take teleport. Tryndamere destroys turrets late even if he was behind. Try to out rotate him, buy lots of vision, and just try to be wherever he isn't.
Take jungle camps when you're too pushed in or can't farm, look for a roam on mid or with your jungler to get some kill/assist gold there.
Even if you lose the lane and your turret and you're just getting pushed all game, you can at least delay it by existing and trying to get CS.
A good jungler will see what's going on and help you out. A good mid laner will see what's going on and help you out. If you don't have a good jungler or mid laner, you did your best and that's all you can expect of yourself -- gg, go next.