Is a spinlock lock free?

Anything that can be called a lock (exclude other threads from a critical section until the current thread unlocks) is by definition not lock-free. And yes, spinlocks are a kind of lock.

If a thread sleeps while holding the lock, no other thread can acquire it and make forward progress, and spinlocks can't prevent this. The OS can de-schedule a thread whenever it wants, even if it's in the middle of a critical section.

Note that "lock-free" isn't the same thing as "wait-free", so a lock-free algorithm can still have stuff like cmpxchg retry loops, but as long as one thread succeeds every time, it's lock free.

A wait-free algorithm can't even have that, and at most has to wait for cache misses / hardware arbitration of contended atomic operations. Wikipedia's non-blocking algorithm article defines wait-free and lock-free in more detail.

I think you're mixing up two definitions of "blocking".

I think you're talking about a spin_trylock function that tries to acquire a spinlock, and returns with an error if it fails instead of spinning. So this is non-blocking in the same sense as non-blocking I/O: fail with an error instead of waiting for resource availability.

That doesn't mean any thread in the system is making forward progress on the thing protected by the spinlock. It just means your thread can go and do something else before trying again, instead of needing to use separate threads to do something in parallel with waiting to acquire a lock.

Spinning in an infinite loop counts as blocking / not-making-progress. For this definition, there's no difference between a pure spinlock and one that (with OS assistance) sleeps until another thread unlocks.

The definition of lock-free isn't concerned with wasting CPU time / power to make room for independent work to happen.

Somewhat related: acquiring an uncontended spinlock doesn't require a system call, which means it's a "light-weight" lock. Some lock implementations always use a (relatively slow) system call even in the uncontended case. See Jeff Preshing's Always Use a Lightweight Mutex article. Also read Jeff's other posts to learn more about lock-free programming, because they're excellent. So good in fact that the [lock-free] tag wiki links to them.