Your choice of client engine should have nothing to do with what you are asking.
If you’re not running an authoritative server client, and you clearly aren’t, implement your own services or ask something like Photon to handle it for you. No game engine will give you out-of-the-box matchmaking and lobbying (unless Amazon has added something interesting to lumberyard, but I haven’t seen anything about it).
When using a “main client” style solution, especially one that adequately supports host migration, you will most likely go through the whole process yourself. Again, that’s not something that is generally immediately supported, as your title specs really matter and there aren’t a ton of generic stuff going on.
