One main advantage of LiteFS is being able to deploy a SQLite-based application and not have downtime during deploys. This is especially true in ephemeral systems like Kubernetes where pods will rollover.
Another use case is moving data close to users. If you're only targeting users in a single country then it's not as big of a deal but RTT from the US to Europe is ~100ms and US to Asia is ~250ms. That's a big latency hit depending on what you're trying to do.
It might be interesting for embedded scenarios where you need an always-available database but can't guarantee there will be a connection available consistently to a central database server.
Another use case is moving data close to users. If you're only targeting users in a single country then it's not as big of a deal but RTT from the US to Europe is ~100ms and US to Asia is ~250ms. That's a big latency hit depending on what you're trying to do.