I use 5.56 LC brass for my Service Rifle, but have some Lapua on hand, so I did a little experiment today.
First, I weighed them, as a rough measure of relative case capacity. Not surprisingly, Lapua is about 4% heavier than LC (ave = 6.20 vs 5.94 grams, respectively), indicating about 4% less powder capacity (assuming a direct relationship between case weight and capacity), or about a grain.
I then loaded some Lapua and LC cases identically, using my standard SR load (77gr SMKs over RL-15, and CCI BR primers), chrono'd them, and found the Lapua cases ran 47 fps faster than the LC cases (2,632 vs 2585 fps, respectively).
Using
Nosler's load data as a guide, I calculate a 47 fps gain is akin to adding an extra 0.4gr of powder to LC cases.
Even in Lapua brass, my load load is within max, but if you're at max before using Lapua brass, using it will likely take you over. Also, I didn't check to see if the extra fps affected accuracy, but if switching to Lapua, I might (or might not) have to make some adjustments.