I've had some issues with my 88 XJS right side door handle. It latches fine when the inner portion of exterior handle releases but lately, it's been getting stuck in the up/open position. Then when closing the door, the latch doesn't catch. If I manually pull down the handle, it closes fine. But this was an occasional issue.

NOW, I had the total car striped and repainted (stunning piano black) and since the handles have been re installed, the right handle always sticks and is actually quite difficult to "unstick" so the door is hard to close.
Oddly enough, the boot latch does the same thing. If I don't pull it back down it won't close.

Would a good puff of graphite help? Or WD-40 lubricant be better?

 

Door first:
There are at least two potential sticking modes:
1 the latch on the end of the door, or
2 the actual handle and its operating rods

If the latch, How it should work:
when you open the door, the latch should stay in the 'open' effectively 'cocked' position. So that when you shut the door again, the catch on the B post should push the latch back to the closed, 'latched' position. With the door open you can simulate this by using a screwdriver to simulate the catch on the B post (push it into the gap in the latch) and see if it is all working properly. Remember you will have to operate the door handle to open the latch after each simulated closing.

If your door will not close, it sounds to me like the latch mechanism is returning to the 'door closed' position, rather than staying in the 'cocked' door open position. The door will not close unless the latch is 'cocked'. My guess is that the interior links between the latch and the handle are incorrectly adjusted, and therefore causing the problem.

If the door latch seems to be working OK, it might still be worth loosening the retaining screws on the latch exterior (not removing, just loosening) and wiggling it a bit and tightening them and retrying.

Door handle
The door handle is connected to the door latch mechanism on the inside of the door (the bit that the exterior latch parts screw into) by two rigid wire rods. These rods can get displaced, half fall out of their holes etc etc. The only way to get at them is to remove the door trim and then drop and skew the window in its track by removing the latch-end in-door window runner. This JUST allows access. The runner is secured by one big bolt through the door towards the bottom and a self tapper at the top that come in from the outside of the door end. Looking at all this makes you wonder why the door opening mechansim ever works!

If you disconnect the rod that is operated by the door handle, and then try the latch, you will be able to see if, disconnected, the latch does stay in the 'cocked' position. If it does, a bit of fiddling with the rod, which IS adjustable at the latch end, is called for. Of course it is just possible that the handle itself is bent somehow. You can test for this too once the rod is disconnected, it should flop about basically.

I am well up on this ATM because I recently spent 2 painful whole days with a VERY patient friend helping me, sorting out a similar problem!

 

Now the boot!

This should be a matter of removing the plastic lock trim cover inside the boot lid and squirting some WD 40 followed by some grease into the mechanism!

The boot lock is easy to remove and very obvious, so it could also be something overtightened, a bit of paint blocking the hole through which the handle goes etc etc. But much easier going than the door...

 

Thank you for all the great information.
As it turns out, my bodywork/painter had to go back into the door after all because when he lowered the windows, they failed to close all the way. It seems there was something catching in the window mechanism on both sides, he said there were several cables that may have not been completely put back in place. I'm hoping once this is sorted out, the door works properly.
If it doesn't, I guess I'll be giving your suggestion a try!
I must say the issue seems to be confined to the exterior handle. If I pull the actual handle back down after pushing it up to open the door, it will close properly I really dread having to adjust rods ans such! I'm great at most repairs but these finicky adjustments usually get the best of me!!