Yes, you can ride on the track. You need to take a class first, either the track training course if you haven't got a history of USAC track racing on other velodromes or the accelerated Saturday course if you do (the latter just talks about rules unique to this class, and helps screen for people who don't know what they're doing). They do have some rental bikes. Then you have to ride in the sessions when you are eligible to ride (e.g., as a beginner, as an established track rider, or as an elite). See www.lavelodrome.org for details.