Thanks that’s very clear.
So basically whenever the LSP wants to use on-chain funds that aren’t in the factory, they just keep this fully separate from the factory and import them into normal channels.
This is a drawback, because it means the LSP would need to have multiple channels per-user, which defeats the goal of using less utxos for more users. But LSPs could opt to never use normal channels and only work inside factories, with the downside that liquidity requests sometimes cannot be satisfied…