Runs louder than normal when accelerating

I'll bet you have a leak in the lower EGR pipe, see pic. It's very common in these cars, that they get that at some point. The pipe is attached to the right side exhaust manifold right before the flange to the cat. The other end is attached to the EGR cooler at the backside of the engine. Almost impossible to get to.
To verify if this is your problem, get a small camera down there, you'll see black sooth on the pipe if it's leakin.
Some say you have to drop the tranny to get to the pipe, others can contort their arm to get behind the engine and loosen the screws.
My best bet is, to raise the car on stands (or on a lift) and take the right side cat off. This should give you enough room to get at the EGR pipe from under the car, using extensions and flexible links on your socket wrench.
You will need new gaskets for the cat (90917-06043,90917-06072), new gaskets for the EGR pipe (25628-50010,25634-50010) and ofcourse a new EGR pipe (25601-50060).
It will set you back approx 150-200 USD.

Mobip, That is excellent advise. Great explanation and quite
advanced I would say. I am going to give this info to the Lex
dealer who does all my work. I bought this car for $6900 a few
months ago and between the ding/paint work, rustproofing the paint and underneath, complete maintenance and repairs I up near
$20k by the time I'm done. Crazy huh? Thanks to all you guys.

I'm glad you find the answer usefull.
It's worth noting, that the EGR pipe develops the crack, because of thermal expansion and contraction, AND vibration. It's a sign that your engine mounts are going bad. You may experience minute vibration in the steering wheel, gear lever and pedals. Get them changed (2x 12361-50100), and the tranny mount as well (12371-50060). Then you don't have to get another EGR pipe in 1-2 years time.
Jimmyc, your LS is cheap ;-) my 95 LS is running into the $30k's now, and counting. But the smooth ride is worth it all.