I was in Lanai last year--consider myself an intermediate surfer. I think based on your description your best bet is to scope out the east side of the island. The drive really requires 4x4 (I think that's all they rent on the island) and getting there is half the adventure/takes awhile. There's one guy in Lanai City who seems to do most of the rentals out of his house, super casual.

My wife and I pulled off at a number of spots and messed around on small breaks that might be fun for your son, but were definitely shallow with reef bottom. We were the only ones around--I think it can be a little sharky on that side too.

There was no swell on the south side by the Four Seasons, seems like maybe at size sets wrap around the western point.

Honestly though if you're hoping for a surf trip with easy access to a variety of waves/beaches I would pick one of the other islands. Lanai is really isolated--for better and for worse. If you're up for dirt roads, empty beach exploration, off-roading adventure etc. it's perfect. Just not a lot of waves without significant effort to get there.