I solved this by running thelounge behind ZNC (to be fair, I already provided ZNC accounts before thelounge existed, so it was already there) and use locknetwork to limit my users to connections to my ZNC server where I have better control over the networks (at least it has a "Max IRC Networks Number" you can set per user, although users could in theory have that set to, say, 3 for Quakenet, Freenode and EFnet, and then change all of these connections to the same IRC network, but it's something).

As far as I know, thelounge itself currently does not have a way to enforce a limit on the number of allowed networks per user.
You could remove the "add network" GUI element though, either by editing the stylesheet to hide it or actually remove it. The latter might require running from source though.