GPv2 should work on any layer 2 that is EVM compatible with all the liquidity sources native to that layer.
As for cross l2 liquidity this will likely only work natively if some party is willing to “abstract away” the cross chain delay and offer the prices it can find on a different side chain for mainnet or whatever chain GPv2 runs (as the settlement itself has to happen atomically in one tx).
We might be able to design more complex “smart contract orders” for the system, where the sell tokens are locked for a certain amount of time and proceeds can only be claimed after some time (enough for a MM to move funds from another l2 while potentially posting a bond for fulfillment).