A linked list + hashtable of pointers to the linked list nodes is the usual way to implement LRU caches. This gives O(1) operations (assuming a decent hash). Advantage of this (being O(1)): you can do a multithreaded version by just locking the whole structure. You don’t have to worry about granular locking etc.

Briefly, the way it works:

On an access of a value, you move the corresponding node in the linked list to the head.

When you need to remove a value from the cache, you remove from the tail end.

When you add a value to cache, you just place it at the head of the linked list.

Thanks to doublep, here is site with a C++ implementation: Miscellaneous Container Templates.