You really can't do much to most champions should they hit you with their lockdown, but your passive and Q slow allows you to kite most champs with relative ease, you just need to remember which abilities are dangerous and play around that (think darius or sett E).
Once you get sunderer no tank can kill you, the sustain is just too strong. Most of your damage is coming from your auto attacks, so use ult and E as a positioning tool rather than an execute. Once you get ravenous hydra you can start pushing in waves and getting that CS score right up.
Against juggernauts and fighters you never really get the upper hand, you are entirely relying on your own ability to dodge their important abilities and kill them before they can kill you.
In teamfights you don't have much survivability until steraks, so you mainly want to go in and assassinate their backline, using ult as a powerful escape tool over walls.