Any action that has housed a 416 Rigby will work with the Lapua.
That includes Rugers, Wby, CZ/Bruno, Enfield P14's, and possibly HOWA's.
My guess is that Savage will come up with a LA rifle in the coming season. They seem to be right on top of shooting trends and the Savage is easily modified to handle the wider cartridge. That was shown when they did limited production of the Lazz monsters.
If you can find actions that housed the RUM family, that would also be a good base for modification.
The Rem700 action looks closer to reality as well.
Lots of choices.
Jerry