It sounds like there could be a ground problem. A weak ground could cause this issue. Different vehicles also have different power capabilities so testing with another vehicle does not always indicate where the problem is.
What you will want to do is test the vehicle without the trailer connected. You are going to need a meter to test the voltage on the trailer wiring harness on your Lexus. If you need a meter we have # PT89ZR. First, test the running light wire going into the converter... view full answer...