The intent is that the LSP makes a probabilistic bet that most users, most of the time, can have their hardware awakened so the LSP can use offchain funds to provide liquidity. This also means that we probably need to handle at most 2 channels per client: one inside this mechanism, and one onchain (which you JIT-open or JIT-splice to if the other clients cannot be awakened inside this mechanism). So you might have one UTXO backing multiple clients (the one that backs this mechanism), and for some fraction (< 100%) of those clients, have an additional UTXO for the optional onchain channel (1 + FRACTION x N where the LSP bets that FRACTION < 100%). This is still better than having 100% x N UTXOs for N users.
The onchain channel itself can be infected with a CLTV branch for the LSP so that after the period, the client has to move to a new factory and consolidate both channels into a single channel inside the next timeout-tree-structured mechanism.