The Sako L61R or AV actions will not be long enough or have a large enough bolt face to build a 338 Lapua on.
Cheapest way to build a Lapua is on a CZ 550 purchased in 416 Rigby and then rebarreled.
Best way to go is with a custom action PGW, McBros, Nesika, Dakota , MRC or Gallin, all of which can be easily made to fit this caliber, unfortunately all are fairly spendy for cost of action