2000 Buick Lesabre 160,000 miles
My LeSabre makes a thump noise when I let up the brake from a full stop. Not when applying, just when letting up.
At first I thought it was a lower control arm, but upon inspection, this does not appear to be the case. The control arm appears to have been replaced before, the pin for the castle nut was missing, and the keeper was not bent over the nuts. I had replaced the wheel hub earlier because whoever worked on this car before managed to cross-thread 2 of the studs,
While I had it apart, I noticed a lot of play in the outer CV joint. Could this be the cause of my thump?
This would be on the passenger side.

It could be. Try the same thing while turning sharply each way . . . see if the thump changes at all.

I tested while sharply turning.
There was no thump with the brakes when used while sharply turning, only going straight (or nearly so)

Almost want to think engine mounts. Open the hood up, put foot on brake and shift from D to R to D to R while watching the top of the engine.

I think you called it with the motor mounts.
When I shift back and forth, you can see the engine more more than I would expect.

If you could post a video on YT and post the link here, that would help out a lot.

Well I replaced the one motor mount that is easy to get to, and, while the thunmp is not gone, it is greatly reduced.
The lower control arms may be on their way out, I do not know when they had been replaced, nor the quality of the replacement part.
Since today is probably the last descent day this year for working on the car, I'll probably have it done.
The old mount was torn in the same way you see in the youtube videos. So, it needed replaced in any case.

Good, your making headway.

Yes, your cv axle is bound when braked. then you let off the brake, freeing it up and because it has play, it makes a noise. however, a torque axis mount in the front of engine bay also can likely do the same thing ESPECIALLY if you hit the gas when you let off. The engine and trans move relative to the craddle not the car. the craddle ideally is bound to the car well, with lower control arms bound to craddle too. If you have a discrepency in play enough on LCA and the engine mounts, the whole engine twists up toward the rear of the car while the weight of the car is pushing the lower control arms down and forward and the transmission is spinning the cv axles and you get a thud from one or more components in that relationship moving