See https://github.com/pixelspark/catena for a SQLite-on-blockchain implementation
LF isn't a wrapper around SQLite at all. It just uses SQLite for meta-data and index information because it happens to be a very capable database and because the ability to do relational queries saves a ton of time vs. hand-rolling such queries on top of something like LevelDB.
The last issue is something I've never understood about cryptocurrency code bases. Why do they insist on implementing a slow ad-hoc relational model on top of a simple KV store when they could just use SQLite? I assume it's because they assumed SQLite would be slow, but it's really not unless you are doing massive numbers of writes.