I don't have a load specific to the Lapua, but I do have one for the .338 RUM. Given that the RUM case is slightly smaller, it should be a decent starting point.
Repeat, these loads are for the .338 RUM!
H4831SC, 90.5 grains, 3095 fps
WC852(s), 97.6 grains, 3236 fps (max load)
H1000, 103 grains, 3106 fps
Some of these are "warm" loads, and should be worked up to. My RUM likes WC852 and 4831 for that weight bullet, It's a fairly "full" load. I'd expect something similar, maybe leaning towards a slightly slower powder if your barrel is longer. Mine's 26".
Hope this helps!
Mark in Utah