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I've fixed the commenting, and cache_info use.
I've left the element management in pure C as it reduces memory use (56 bytes for 4 element list, vs. 16 for lru_cache_elem), and avoids ref counting overhead (3 refs per link, plus GC). The difference might become quite marked for very large caches. There's also a nice invariant that links the key to the cache dict, and the result object to the lru_cache_elem. I'm happy to change this if it doesn't matter.
My only concern now is the wrapping of the lru cache object. In the Python version, @wraps allows the lru_cache to masquerade as the wrapped function wrt str/repr. The C version is wrapped, but str/repr remain unchanged. Not sure if this is a problem.