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I had that issue on my daughters RX300 and it was just worn contacts on the starter. $20 fix, but starter needs to be taken off and contacts replaced. They are copper and wear down. Most auto parts stores keep these contacts in stock. Smart to replace the plunger at the same time. That was done 100,000 miles ago and the starter never had an issue starting after that.
Update: The Lexus RX350 2012 had bad cells in the battery. AAA came and jumped the car and ran diagnostics. We replaced the battery and car is running great again. Thank you to both Salimshah and jimbug for responding to my post.