Could be something as small as a worn bushing on an exhaust hangar..... exhaust resting on part of the the frame maybe. As stated... a worn mount can do it too. Get under there and look, feel and listen and wiggle components under your LJ and see if you can isolate it.
~Todd~ 2004 X 4.0 5 speed---SOLD
4" Lift, 4.56's, 33" Duratracs on M/T Classics
RR SYE, Tatton CV, MML, BL, TT, Dynomax Exhaust
Hella Lighting: Driving, Fogs and H4 E-Codes
... and NEVER will be