Hi.
When you say improvement, do you mean fps or in terms of graphics?
earlier i was looking at benchmarks for gtx 980, 1060, 1070 and the 1080. there was around a 60fps difference from the 1060 to the 1080 on Battle filed one and the graphics was just slightly better and richer in colour.
i don't have tomb raider, but i have an i5 7600k and there is little difference in the cpu's.
http://cpu.userbenchmark.com/Compare/Intel-Core-i5-7600K-vs-Intel-Core-i5-7500/3885vs3648
i don't think it has anything to do with your TV, but maybe try a slightly lower spec tv or monitor you have lying around and see if your 4K was too much for your pc to handle. RAM honestly doesn't matter in my opinion, i have 8GB.
I will be buying the ASUS 1070 Dual in a few days. have you changed your slider settings in the game menu?
again, i don't know much about the game, so i'm sorry if this means nothing.
i hope it helps, and your problem (if you want to call it that) gets resolved
regards
Marc