Ok, now I know what you are using.
I have a Vanguard in 300 Weatherby. I have never measured the bolt to determine if it can go as far as 338 Lapua.
It's well past bed time (2:30am) and I'm done in the shop for yesterday.
Later today I'll get out the VG and have a look.
The biggest challenge is the extractor. There is no extractor for the .590 bolt face of the Lapua for the VG bolt. You will have to customize.
If you single feed, the magazine is not important. If you want to mag feed, again some customization will be required. The follower won't be quite right, the feed lips of the magazine box will have to be massaged. There are plenty of loads for the Lapua that are shorter than 3.56. Again, I'll have to measure the mag box to see what's up there.
You didn't say what the intended use for the rifle will be. Hunting, "target" or 1 mile plus?
Since I have experience in this area I'll opine a bit. Converting a Vanguard to 338 Lapua is more work than it is worth. I have 4 Vanguards and love them but there are easier and more cost effective roads than that one.
I have an alternative suggestion for you if you want a 338 but are not married to the Lapua. Try a 338/28-Nosler. I have one and love it. No modifications required. It will just work. Depending on your intended use and barrel length you can achieve very decent performance and every load should mag feed.
Example: With a 28" barrel, 300grain Berger Hybrid over IMR7828 should reach 2750fps. That would keep the bullet well supersonic past 1 mile.
or if you are hunting
Example: With a 24" barrel, 185 Barnes TTSX over Reloader 17, 3250fps. Starts with muzzle energy over 4000'lb. with a 325yard zero "flat" to almost 400 yards and at that point would still have well over 2000'lb impact energy and impact velocity of 2350.
I have shot many combinations of bullets with the 338/28-Nosler. I have confidence in my data. I killed a cow elk a couple years ago with it.
Another alternative is a 338 RUM. There are hunting loads that will mag feed. "Target" loads that will make a mile or more. It's a bit crowded in the magazine length department but it will work. Speed will be between 50 and 100fps faster than a 338/28-Nosler.