I have nice Leapold Scope on my Rem 700 LA.   I just finished building my AR15 flattop.   I can't afford another long range scope for the AR, so wanted to explore the possibility of using one scope for both rifles.  I know the rem would need some kind of picatinny base, and then I would need some kind of lever operated quick disconnect scope rings.  Scope is 30mm.
Any suggestions on what to buy.

Don't have an answer, but think you're going to have a height issue.  The scope centerline on the AR wants to be 1,40 inches above the rail which is the same height as standard iron sights.  That height works for most people.  The scope height on a typical bolt gun wants to be a lot lower––maybe .75 inces? (its been a while). Without physically moving the scope from one mount system to another, its not obvious how you're going to make that work to any reasonable level of satisfaction.  A compromise height would just give you a crappy solution on both rifles.

If you just use rings that screw on im pretty sure screwing on screw in 2-3 turns, then screwing the other one in 2-3 turns until each are tight would get it back to zero every time. Not sure about a base for the rem.

Picatinny base on the 700.

Extended riser rail on the AR flat top.

LaRue medium height rings.

Yeah, something like that oughta work.  Good thinking.

That's the best option - an extended rail or riser on the AR, and good QR rings on the scope, but you might have a trade-off to get the right height on both.

You'll need 1.4" or so centerline on the AR, as skipsan says, and most rails are 0.5" (though a few are taller, like the RRA at 0.67").  You'd want to use rings high enough to get you to 1.4" on the riser, and they'd likely be a bit high on the other rifle, depending on the scope, but it'll work.

The other problem is keeping track of your zeros for each rifle.  You'd zero it on one, then swap it to the other and re-zero, making a note of how many clicks and which direction.  Once you had that, you'd change it that much each time you swapped between rifles, then send a few downrange to make sure it's good.  After a few tries, you'd have a pretty good idea of how stable it is.

I used to do this on a few rifles, but honestly, it's a pain in the butt, and I've ended up buying more scopes that cost less to help avoid it.  YMMV, as always!