There is also a county park on Lopez, Odlin CP. Gorgeous views, nice beach, etc. Lopez is a super relaxed island community, less touristy than a couple of the others. If you can swing a reservation either there or at Spencer Spit SP that would be best. I mean, it’s an island, so you’re taking your chances if you show up just hoping for a spot. Not to say it couldn’t happen, but those ferries get expensive for vehicles with trailers.
When we visited there two years ago, we parked our Escape and tug at the Anacortes ferry dock then bicycle camped the San Juan’s, including Lopez. There’s always room for another cyclist tent to squeeze in without a reservation!