2012 Lexus RX 350 - Starting issues

Trouble with push button start. Maybe I need a new battery as the 2012 battery is the original?

Very likely you need a new battery. Have the old one checked before just buying a new one though.

Push button start problems are very rare, battery failure is quite common. 7 + years is a reasonable life for a battery, I replaced one yesterday in a 2015 RX350.