If there would be a hard fork, the outputs funding the lightning channels would exist in the UTXO sets of both networks. If both channel participants run Lightning Network software compatible with each network, they could maintain both versions of the Lightning Network channel. However, it would probably require a novel solution to distinguish the channels on the two separate networks. If at least one of the participants does not want to use the channel one one of the networks, they would likely try to close it. If transactions between the two networks are replay-safe, they could close it only on one network, otherwise, they might close it on both and open a new one only on one network once they have acquired coins that only exist on one network.