I would think that anything that can handle the size and pressures from the 300 R.U.M. can handle the 338 Lapua (the RUM has higher case capacity then the 338 Lapua), but I'm not sure if there isa bolt face size issue. That having been said I would expect that any Long Action capable of handling the 300 RUM should be able to accomodate the 338 Lapua, like Weatherby, Winchester, Remington, Sako, Neseka.
spade buy the sig r93 blaser, I shot one the other day and it is a dream come true. It is almost orgasmic, it is more accurate than anything I have come across and the straight bolt is a sweet, smooth operation.
Not all actions can chamber the big .338 Lapua. The Lapua is built on the .416 Rigby case. It does have a large case head diameter, and a long OAL. The remington 700 can be modified to accept it, but the work is fairly extensive, and IS NOT RECOMMENDED in my book. The easiest to get to build one on would be the CZ550 big magnum action which you can buy bare from Brownells. I would use that one or possibly a sako action, as their big magnum action is also setup for the Lapua. Weatherby is another alternative.