1993 Lexus Ls 400 Acceleration Problem.

When accelerating to merge onto highway, the engine "lugs down" when gears shift from low to second. Problem will persist as long as I keep my foot on accelerator. If I let up for a few seconds and accelerate slowly, it recovers but not until vehicle slows down somewhat. Not good with traffic behind. Was told by a mechanic (not Lexus) that the problem was with the catalytic converter(s). Took car to a muffler place where they tested (cut small holes in tail pipe before and after both converters(?)) and said the converters were bad. I spoke with a Lexus mechanic who said he didn't believe the problem would be the converters. The car has about 110,000 miles and runs good otherwise. YOUR OPINION/IDEAS, please. My next step is to take it in for diagnostics. QUESTION: Would I get a better result taking it to a Lexus mechanic rather than another repair facility with diagnostic equipment? The other place I have in mind is a Firestone shop. Thanks for your help, Jim