Depends. If you run a max or hot load in Lapua or Win brass, and load it in LC brass, you will get pressure. LC is very thick, and has less internal volume than Lapua and Win. Win and Lapua will have similar results, but Win brass has slightly more case capacity than Lapua. Pick one brass and roll with that one.
i have had done a water capacity test with different .308 cases. didn't do lapua, but did federal, winchester, and hornady-match. federal had the smallest capacity, winchester and hornady-match were bigger. winchester brass is supposedly prized by the LR guys because of this because you can jam more powder in.
in practice, FC brass gives me higher velocity with the same charge compared to winchester and hornady brass. winchester and hornady give the same results - not too surprising since they seem to hold within a few percent of the same water capacity.
Thanks for all the replies guys,I have been using lapua brass, with br2 primers and 44.2 grams of varget with great success for a novice reloader. But I have a few hundred win and about the same in LC brass, was hoping to try and mirror the lapua case load without going out and buying more lapua brass. By using either the win brass or the LC stuff which is late sixties or early seventies match and seems very well made.
You really have no idea which way it will go until you know the average water capacity of the two brands of brass as fired in your chamber.
Remember to have them trimmed to the same cartridge length first. If you are using the Lee through-the-flashole trimming system, just save and re-seat your COMPLETE fired primers and watch for water leaks. Clean that scale tray between weighing if needed.