I own a 2000 Lexus RX 300 with approx 26,000 miles that I bought new.
About a year ago I started getting P0171 codes but the Lexus Forum
cured that problem by cleaning the Mass Air Flow Sensor with contact cleaner.
Recently I started getting a code P0125, P1150 and P1155.These are
apparently related or overlapping. Has anyone had the P0125 problem
and what was the solution. Some have suggested that a sticking
thermostat may be the culprit. Any suggestions. Is replacing the Thermostat
a DIY job like in the good old days before things got so complex?

 

Welcome to the Club.

Focus on P1150 and P1155, those are the key codes.

P1150 is related to the Air/Fuel sensor on the Bank 2, Sensor 1. That's visible in the engine compartment as shown below.

 

P1155 is Bank 1, Sensor 1 behind the engine shown below.

 

P0125 and more often P0171 usually comes up when you get a/f sensor issues like you have got, but the A/F sensor codes are the ones to look at first.

I'd STRONGLY suggest you get access to an advanced OBD2 scanner to see what readings are seen on both the front and rear A/F sensor. Most mechanics have one of these and they can tell if it's on the fritz or not. A generic OBD2 scanner is not sufficient for this task.