Hey
This may seem arbitrary, but I may have an answer for you.
This same type of problem happened to me about a year ago. This smooth world class car started balking, cutting out, lurching, and seemed ready for the junk yard. It happened all of a sudden. No warning.
I thought the engine was toast.
Now it's smooth as silk w/ 255,000 miles on it.
Open the trunk. On the left side you will see a wire harness on the left hinge. After repeated openings and closings the wires inside that harness become fatigued and frayed. Then they start shorting out. Then your ECU starts getting bad input. Then your air/ fuel ratio goes to hell, then you have intermittant spark. Then sputtering, stalling, and everything you describe. This is a design flaw and lexus knows it.
In short ( :D ), if this describes your problem, then strip down the harness, untwist all the wires, re-connect, then re-tape with duct tape.
Make sure to leave off the bracket that ensures tension on the harness. Just let it swing free and loose.
In my case, problem solved, and no spending thousands of dollars in diagnostics, parts, and tech snafus.
I am 95% sure this is the answer. Best of all, it's free!
Good luck...