Some considerations can be similar, but the total set of details are different.

It also depends which lock free solutions you're evaluating.

Some are higher order spins (more similar high level problems), others have different secondary costs (such as copying). A common overlap is the inter-core, inter-thread, and inter-package side effects of synchronization points, for a lot of stuff with a strong atomic in the middle that'll be stuff like sync instruction costs, pipeline impacts of barriers/fences, etc.

There are several classes of lock free algorithms with different properties.

Lock free algorithms for read only access to shared data structures have only seldom disadvantages (when the shared data structure is modified extremely frequently by writers, so the readers never succeed to read it between changes), so for read-only access they are typically the best choice.

On the other hand lock free algorithms for read/write access to shared data structures must be used with great caution, because they frequently have a higher cost than using mutual exclusion. Such lock free algorithms are based on the optimistic assumption that your thread will complete the access before the shared structure is accessed by another competing thread. Whenever this assumption fails (which will happen when there is high contention) the transaction must be retried, which will lead to much more wasted work than the work that is wasted in a spinlock.

Lock free algorithms for read/write access are normally preferable only when it is certain that there is low contention for the shared resource, but in that case also a spinlock may waste negligible time.

The term "lock-free" is properly applied only to the access methods based on optimistic access instead of mutual exclusion (which uses locks).

However, there is a third kind of access methods, which use neither optimistic access nor mutual exclusion with locks, so some authors may conflate such methods together with the lock-free algorithms based on optimistic access.

This third kind of access methods for shared data have properties very different from the other two kinds, so they should better be considered separately. They are based on the partitioning of the shared data structure between the threads that access it concurrently, so such methods are applicable only to certain kinds of data structures, mainly to arrays and queues. Nevertheless, almost any kind of inter-thread communication can be reorganized around message queues and shared buffers, so most of the applications that use either mutual exclusion with locks or lock-free optimistic access can be rewritten to use concurrent accesses to dynamically partitioned shared data structures, where the access is deterministic unlike with lock-free optimistic algorithms, and there are no explicit locks, but the partitioning of the shared data structure must be done with atomic instructions (usually atomic fetch-and-add), which contain implicit locks, but they are equivalent with extremely short locked critical sections.

In a very basic case lock free data structures make threads race instead of spin. A thread makes their copy of a part of list/tree/whatever it needs updating, introduces changes to that copy and then tries to substitute their own pointer for the data structure pointer if it hasn't changed in the meantime (there is a CPU atomic instruction for that). If the thread fails (someone changed the pointer in the meantime) it tries again.