Scott,
I realize that now for the U18. If Lyon's parents aren't members at Oak Hill and he's a member, then that's amazingly awesome.
If you want an U18 membership in America, 99% of the time it's going to be at a public course paying an annual fee.
My father is a member at Oak Hill, meaning a few things. First, I can play under his membership with the purchase of a tag. The club has different tags for different levels of junior players and for different costs. Second, my playing hours have some restrictions, depending on what type of tag I purchase. Third, I can only play under my dad's membership until I am either 25 or gainfully employed. You cannot have membership status at Oak Hill until age 18. It is a good setup because I can play unlimited golf under my Dad's membership. However, I will not have that privilege for much longer, and I certainly will not be able to afford membership at Oak Hill after I am out on my own.
I believe this is how most memberships work for juniors/minors in the US. I know very few people my age who are members of big clubs on their own. One of my buddies is a non-resident member at Fox Chapel and has been so for a couple of years. However, most kids my age are playing under their parents' memberships at clubs. There are some clubs that don't allow kids to play until a certain age. I think the minimum age at Laurel Valley is 16, for example. I always found that silly. It does not make sense that a middle-aged 25 handicapper could play a course that a 14 year-old scratch golfer could not.
I rather like how things work in Britain for golf. I could NEVER join a highly-regarded club in the United States at age 20. I would not have the funds. Yet I am able to do so over here. As it stands now, the private club system in the US does not encourage younger golfers to club members on their own.