Okay, so, I can't take screenshots on my Kindle without downloading some shady app, so I'll do my best to describe what I did:
I took the Lizahrd altar, and built a little arena. The lihzahrd altar was within a small room without background walls and without a ceiling (at first)
After you summon him, immediately build a roof over his head. If you stand right above him, he won't shoot his deadliest weapons- his lasers- at you. They always killed me before I got good stuff
I also put in some traps after I got a picksaw, like flame and super dart traps, instead of walls so that I could hook them up to a 1-sec timer and automate my farming. You really need a nimbus cloud or a crimson staff, because if you put the clouds right on the blocks above him, the rain particles will go through the ceiling and hurt him. You need to be careful in the second stage where his head detaches and he shoots lasers at you regardless.
I would recommend using turtle armor, and if you have a death sickle, use that too, because its projectiles will travel through blocks.