Can you join in a new game, without split screen to start with?
Have you tried switching who is hosting?
Have you tried joining by invites, as well as the lobby? For the lobby visibility, if it is set to invite only, try getting the host to increase it to friends only or public.
Have either of you tried playing with anyone else?
Have you tried hosting/joining an Arena match?
Try going into Arena mode, create an arena, open the Connectivity menu and check the settings, then exit to the main menu and try joining in the lobby.
Try clearing the PS4 cache: press and hold the PlayStation button on the controller, select 'Turn Off PS4', wait another 30 second after it finishes shutting down, and start it again.
If you start the game from a different PS4 account, and you or your friend start a new game, can the other join? That would give a separate drive space for saves.
It may help to remove the game profile, on each system: in Settings, Storage, System Storage, Saved Data, select the game, then select 'Profile', press the Options button and Delete. Just delete the profile slot to keep any saves.