The Omnibolt Daemon (OBD) is definitely a fork of LND and it's a btc-compatible fork, which means, the bitcoins in OBD are on the real lightning network, you can open channels to any other lightning user without them needing to run your fork, and you can send them bitcoins over those channels. But the USDTs in OBD require something like a parallel network, with its own set of channels. So I would say that's two networks, the "real" lightning network with bitcoins on it and an "omni" lightning network with omni tokens on it, one of which is USDT.

On the other hand, altcoins have been "on the lightning network" since day 1 (namely, Litecoin) and it is possible to use submarine swaps to transfer bitcoins over that network and "back into" the real lightning network. The same is now true of USDT. Which means the two networks are connected. And if they are connected, are they really just one big network or they still two separate ones? I'm not sure how to answer that but I hope this explanation helps.