These seemingly unrelated problems sound like the old chronic Ls400 trunk hinge issue: http://us.lexusownersclub.com/forums/index...showtopic=50087
"This same type of problem happened to me about a year ago. This smooth world class car started balking, cutting out, lurching, wild rpms, dash flickering, radio went out when hitting the brakes, just seemed ready for the junk yard. It happened all of a sudden. No warning. 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 sputtering, and stalling. This is a design flaw and lexus knows it. If this describes your problem, then remove the plastic bracket on the left hinge, strip down the harness, untwist all the wires, re-connect, then re-tape.. Don't assume they are good- strip them down and examine them. Make sure to leave off the hinge bracket that ensures tension on the harness. Just let the whole mess swing free and loose. In my case, problem solved, and no spending thousands of dollars in diagnostics, parts, and tech snafus. Best of all, it's free. Takes about 30 minutes." Post back what you see at the hinge.
Alex