If it is, then something is wrong. You're 20 years old, for crying out loud. I don't care how overprotective parents are, you have the absolute right to buy what you friggin' want.
If you really want to keep something on the downlow, here's what you do. Buy a $20 Amazon gift card at the grocery or drug store. If your parents ask what you bought, tell them it's a gift card for a friend. Give the card to your BF. He can use it to order lube on Amazon. Simople, done, and nobody lied about it. It was a gift for a friend. Oh, sure, you may not have told them everything but for crying out loud, do you think everyone talks about all aspects of their sex life with their parents?
Spit can work, but it's hardly as effective as actual lube. Since this is the first time and it sounds as though there's quite a restrictive hymen in place, I think "real" lube is a good idea. OP, if you don't want to buy it then have him do so. Yeah, it might be embarrassing the first time but, for Pete's sake, you can even get it on Amazon if you must. Makes it a little less spontaneous, of course, but you should be planning this out anyhow so ...
Hey! Chronic BV and YI here! I switched to a lube called [Isabel Fay](Natural Intimate Personal... https://www.amazon.com/dp/B00Q3GHPUS?) and it totally changed my life. Seriously. Adore it. Obviously double check with your doctor, but it was gentle and cheap and comfortable for me!
Edit- a typo.