will not start. battery seems to be good

OPEN in crank circuit , first step would be to TEST for signal voltage at solenoid. IF getting correct (battery) voltage with key in 'crank/start' position , then most likely starter is bad. VERIFY clean (no corrosion inside--REMOVE cables to check!!) connections at battery! Seen many good techs get fooled by unseen corrosion and an assumption of good contact! (myself included) over the coarse of 30 years it's got to happen!

My 2002 ES300 had a similar problem. Every week it would just not start while at the bank, store etc. I would wait a few minutes and it would start but it was very annoying. All the dash lights worked but the engine wouldn't turn over. I changed the starter and the problem went away. It's not an uncommon problem with a 10+ year old Lexus, possibly on newer cars too. It was about $200 for a replacement starter. It will cost you another $100 if you have a mechanic do it for you. The starter is a bit of work to get to, you have to remove the air cleaner housing and associated hardware, plan on 2-3 hours if you are an experienced guy doing car repairs.