Is there a program that lets you play co-op games with people (with matchmaking or custom lobbies)

Parsec is the only one I am really aware of, at least for turning couch co-op games into online multiplayer games which is pretty cool in itself. I hope someone will have your answer so here's a little BUMP to help you get there ^-^

There is player.me. But I never tried it so I don't know how it works.

Parsec can be combined well with Discord servers for specific co-op games, if you're trying to find people to play with. If a game has a large base of players, you can often find someone to play with pretty quickly. Just google the game title + discord, then ask around for people interested in playing.

Back in the day I used to play DotA over Garena which I believe simulated LAN and also had open lobbies and supported a variety of different multiplayer games. I don't know if it still works the same though since it has been many years since I have used it.

GameRanger - needs game support. Has 500+ at the moment
XLink Kai - global console network. Requires setup and patience