338 LAPUA is too big for a REM 700 action , when you open a rem bolt face to 338 LM you get only a very thin ring of steel around the case head
even if REM 700 action is strong , REM lugs design on REM 700 is not really design to hold big case / hight pressure , 300 ULTRA / 404 case is max for me and never forget it is very difficult to find a human head as spare part in your local emergency hospital .
best is to purchase a real big custom action or use 338/300 ULTRA in single shot on a rem long action , 300 ULTRA cases are far cheaper than 338LM case.
There is a compnay out their that is modifing rem 700 la to work with 338 lm.
You have to open the bolt face and like Dantec said the bolt face would only have a small amount of metal to surround the base of the case. The other thing you have to do is mill out th eback side of the magazine well cutout to accomodate the longer OAL. You must then mill the same amount off the bolt stop and possibly make a new bolt stops as you dont have much before you wont have any bolt stop at all. I think about .375 thou would be max before you had to make a new bolt stop part.
I think that your best bet would be using the 300/338 Ultra, or 300 Tomahawk. Brass is cheap and although it isnt as good as Lapoopa, the money versus the case is just to expensive.
Some friends have built .338 Lapuas on 700s and .338-416 Rigby Imp. also. They work and now have several hundred rounds through them. They are all single shots, no attempt to make them into repeaters. Remington built them but called them the SR8, one has been offered on snipercountry classified board, recently. I really like Remmy 700s but would go with the Wby Mk5 if I didn't want a custom. I have a wby Mk5 with two bolts, one mag and one for the big cases like the Lapua that I'd sell you, new action, never fired before disassembly. Email me if interested [email protected]