Lexus GS Transmission Issues

Those symptoms definitely point to a transmission problem, possibly related to the cooling system. Before assuming it's the radiator oil pressure, have you checked the transmission fluid level and condition? Low or dirty fluid can cause similar issues. Also, what's the exact error code? That would help narrow things down. A bad cable or plug connection is also possible, but we need more info.

Thanks, I haven't checked the transmission fluid yet, I'll do that now. I don't have the exact error code with me. If the fluid is okay, and considering the possibility of a bad cable or plug, how would I diagnose the specific location of that defect in the radiator oil pressure system? Where can I find info on diagnostic procedures?

Given the symptoms and your unfamiliarity with detailed diagnostics, I'd strongly suggest taking your 2006 Lexus GS to a good workshop with the right tools and expertise. Trying to find the problem yourself without enough knowledge could make things worse. The error code is key. A professional diagnosis will give you a clear answer and prevent unnecessary repairs. The repair might cost around 95€.

Thanks for the advice. I was leaning towards professional help anyway. I'll get it inspected ASAP. I appreciate your expertise, and for stopping me from causing more damage. The workshop inspected my Lexus and your estimated cost of 95€ was spot on.