What would you use instead?

By the time you've implemented even a basic key-value store with on-disk storage you've probably written a bunch of code that would be unnecessary if you had used SQLite.

LMDB?

SQLite is superb choice as a local storage solution, you don't need a transactionality requirement to use it as a KV store.

People choose NoSQL databases primarily for scaling reasons, which is not the problem here.