Battle-tested multiplatform support (and thus reliability) is definitely a key selling point. This is further reinforced by its impressively extensive test suite.
Long ago I lost my first Android smartphone's SMS database since they used to delete + re-create even barely corrupted databases, but by now most of the kinks have been worked out.
Plus it's amazingly fast and is packed with SQL features. For such a small lib, it's a miracle. And the way the author talks about it (he is not from a DB background) it so funny.
Sqlite is one of the simplest RDBMSs that you can run on a client, which is really useful for deploying apps that need their own data store
Also Sqlite has native EF drivers which makes it first-class .NET citizen.