Ignoring whether it would be hard/easy, story-wise do you think playing LR before any other DLC would
a) Provide backstory that enhances the rest by putting it in context
or
b) Make the rest of the DLC feel a bit hollow because you've already experienced the climix

Not sure.
Doubt there would be much diff. DLC seems to focus both forward and backward, and I have not yet played it.

Old World Blues had some odd "tapes" of the other Courier talking about eventually meeting the Courier.
I also saw traces of Christine and some unknown Brotherhood person talking about Elijah, all from from Dead Money in OWB as well.
In theory, I amagine one could mod the DLC so it can only be done sequentially.

The latter.

I'm sure Lonesome Road will be great nonetheless, but I'm also sure that all the hype from the other three would make doing the Lonesome Road at the end all the more sweeter.

If storyline is what you are interested in then you should probably go either by order of release or play the other 3 DLCs in whatever order you like, then play LR last, because DM, HH and OWB all "hint" in some way towards LR...

While they can be played in any order, the DLC are meant to be played in order because of the foreshadowing that happens in all of them. It wouldn't make much sense to be asking questions about Ulysses and the Big Empty in Dead Money and Honest Hearts if you've already played Old World Blues and Lonesome Road before hand.

There will also probably a certain feeling of closure you'll get if you play them in order that you wouldn't get if you played Lonesome Road first. Lonesome Road is meant to be the grand finale to the DLC story arc, and if you play it before the others that sense of closure would be gone. The way I see it, the New Vegas DLC is like an episodic game; you can potentially play them in any order but if you want to experience it the way the developer intended then you should play them in order of release.

Considering Ulysses was involved in all of the previous DLC I would recommend playing them in order. The foreshadowing and events that conspired are huge and connected to Ulysses. You can play out of order but the closure you'd get after playing the 3 before would make it all the sweeter. The developer's intended Lonesome Road to be the last thing done in New Vegas (if you ignore Gun Runner's Arsenal) and hints of that can be seen (in OWB a ending slide for a character makes mention that the Courier has one more road to follow and that he must walk it alone; it assumes you've done the 2 precvious DLC as well). It is not necessary to play them in order but you will get more out of it if you do.

Having listened to the latest holotape (3rd), I'm starting to think the devs really want us to play LR last. Think about it, if the Courier listened to that tape before going into Zion and found out about the destruction of New Cannan, why didn't he/she then warn the Happy Trails caravan about it?

I think doing LR first would kill some of the myth building going on in each dlc we've gotten just a little bit more info part of the excitement was trying to figure out Ulysess and playing LR first kills that , it also would create a few inconsistencies ie not warning happy trails about the white legs or new canaan and a few others. I'd do the first 3 in any order saving LR for last.

This. I have to agree with Longknife on this one. Would be a much better experience after the first 3 DLC. IMO anyway.

Hearing all the dialogue that talks about Ulysses AFTER meeting him would be kinda odd. Especially since Dead Money has the "Things to Come" achievment/trophy/challenege.

He's probly going to ask you if you went to these places (SM, Big Mt, Zion) and you're gonna say 'Uh no, I haven't."

I'm personally expecting an big "Oh, wow" moment much like "Would you kindly" in Bioshock.