It does appear to move too much. 2 out of the 4 mounts are fairly easy to do. the other 2 are a pain. You'll need to figure out which ones are bad. But on a 20-year-old car if 1 or 2 are bad the others aren't far behind.
Here's a post that contains a few possibilities:
Metallic Noise When Going Over Speed Bumps / Potholes - Brakes & Suspension - Lexus Owners Club
The engine appears to be rotating more than it should, so worn motor mount(s) is a possibility.
USNews claims the Lexus RX provides 18.4 cubic feet of room behind the second-row seats and 56.3 cubic feet with the second row folded down.
Unlike the 3-row model which keyesLexus.com shows that for the RX350L, with all rows in an upright position, it has 7.5 cubic feet of cargo room. Folding down the third row increases the SUV's cargo room to 23 cubic feet. Congrats, Mike! If your dealer is like mine - they put your Lexus in a special delivery showroom with lots of lights. Then they bring you in to inspect the 350.