The Lyra cartridge is NOT prone to resonating and causing feedback problems. It is most likely the combination of the arm/cartridge/table suspension that is unfortunately tuned to a resonant frequency that is causing the feedback. You could try adding a small amount of weight to the headshell to see if it moves the resonance to a less sensitive frequency, or you can try tuning the table to change its resonant behavior (put it on a different platform, add weights to the plinth, etc.
It probably makes sense to reduce the overall tendency of the platform the table is sitting on shake--if it is on a rack, can you make the rack more rigid? If the rack is close to the wall, the best way to make it more rigid is to somehow attach it to the wall. I did this by putting a cleat on the wall near the top of the rack and then using angle braces to attach the rack to the cleat. This made the stand MUCH more rigid.