Always eager to ride in some new site: I'm always eager to share my technique to check out how worthy is cycling at some new location. Not that you haven't used such a technique. Perhaps, none of us have personal recollections of riding Lassen.?
I checked out the local cycle clubs, shops , or cycling search sites .
The closest town is Redding and it has one bike club. That being the Shasta Wheelman. http://shastawheelmen.org/
The local bike shop describes local cycling options. There are many options outside of Lassen.
http://bestrides.org/ride-locator-map/
Being that there is only one road in and out , should your ride be roadie oriented , that is your only option as to riding the park. Good luck.