Test it first before you lap
The way to eliminate the "probably" is to take a straightedge like a good ruler and put it on edge on the stone (lengthwise) and hold it up to the light. If you can see light between the straightedge and the stone, you need to lap and especially if there's more light in the center of the stone. My guess is a new stone from Woodcraft probably won't need lapping unless something is wrong with the surface. Several folks have gotten Starrett machinist's rulers from me to test flatness this way. These are precision tools that are as flat and straight as ever you need in a ruler.
Question: what are you lapping with? This should not be an arm-busting process with any stone. It should also be fairly quick. I lap about 20 stones a week and have used a DMT 8" continuous diamond Coarse for a couple of years. It makes coticules purr like velvet. If it's a vintage, dished stone I'm lapping, I use a DMT 8" continous diamond Xtra Coarse and that puppy will wear down a stone right quick. Then finish up on the Coarse DMT. Do all this in the kitchen sink with a thin stream of warm water playing over one end of the stone to wash away swarf as it forms. Using a Fine grit stone doesn't work as it loads in seconds and has to be cleaned before you can move on.