Here's some good reading: https://www.lotustalk.com/threads/rear-engine-mount-replacement-tips.475677/

That said, I don't know how bad it would have to get to cause a clunk. Could be a detached exhaust hanger or something like that.

My fix (in that thread) has been rock solid.

 

Borescopes are handy and fairly cheap but really pay off. I've got 4 different ones but the short two head is great for both Lotus. Perfect focal length for searching inaccessible places.

 

UPDATE
Anyway to tell how worn the mounts are? I don't see any obvious signs of them being bad...other than maybe a little discoloration around the nut.

The bottom photo, discovered this bolt is missing... Wondering if that could be the issue?

 

View attachment 1401683
View attachment 1401682

UPDATE
Anyway to tell how worn the mounts are? I don't see any obvious signs of them being bad...other than maybe a little discoloration around the nut.

The bottom photo, discovered this bolt is missing... Wondering if that could be the issue?

I would be concerned. They are a PIA to get on. With my Elise just front and rear were used like many other members.

I think the best way to attack is see if all bolts loosed the others gives enough freedom to get a bolt in. The hole might be buggered from previous attempts, see if you can visually check. If using prybars doesn't help get that bolt in get a floor jack to lift and wedge as needed. You might have to loosen all motor mount bolts to get enough freedom to get bolt started.
Might be good to pull that mount and see if bolt will thead in , if not then take a tap and chase the hole.
Start a cuss jar you could have your next mod paid for by the time you finish LOL

 

One clunk my car developed was from the sway bar bushings going bad. I would hear a clunk any time the car went over an uneven surface like entering a driveway at an angle. I don’t remember if it happened in a straight line under acceleration, but if the bushings are bad enough, it could definitely happen.

It’s fairly easy to check if the sway bar bushings are loose. On level ground, grab the end of the sway bar and see if you can move it left and right (in the car’s orientation). If it moves fairly easily and makes a clunk noise at the ends of travel, you’ll probably want to replace all four sway bar bushings. My car became much quieter once I replaced mine a few years ago. Relatively inexpensive and simple to replace, so I might suggest it even if it’s not the source of the clunk you have today.

 

The first photo is concerning as well. All of those aftermarket mounts should position the thru bolt in the center of the red polyurethane insert. Yours isn't. That looks like significant wear.

For the two lateral mounts, just replace with stock- they're more than adequate in those positions. You should be able to find them on eBay in good condition. The front and rear benefit from some extra stabilization. I haven't attacked the front one yet, but if you're interested to run the S1/S2 hybrid I came up with for the rear shoot me a PM.

 

Shape eye first photo.

 

I bought a set of those mounts when I was reinstalling my engine. During installation one of them fractured. I think I ended up using 2 of them, reusing the left upper stock one then rebuilding the right upper stock one. With that and the failures that have been posted here I would not purchase those aftermarket ones.