I Hate to be a doom monger but whatever you do don't take it to Lexus. A pal of mine with a GS300 did take his car to Lexus with a remote issue like yours, 12 weeks later and £2,500 lighter he got his car back. Lexus stripped it down and then could not get it to start, new CPU's etc etc had to come from Japan.
if you can put up with it then do so, otherwise it could cost a Bomb