Eng rpms go up.

It's normal for the idle speed to rise when the A/C is on but the engine shouldn't run rough. I assume that the check engine light isn't on or you'd have mentioned it. I'm thinking that the A/C compressor may be seizing up and causing the engine to stagger or there may be an ignition or fuel problem. If you want to find a Lexus specialist, here's our directory link for you: https://repairpal.com/lexus-repair-in-knoxville-tennessee