"Wouldn't the new license be a good indication that the 2nd Las Vegas Club really wasn't related to the original Las Vegas Club?"

Yes. IMO.

I'm pretty sure the same people could have moved the license across the street. The LVC had a very early license, under 10 if I remember right.

The FQ's had something like 17 different parcel owners if I remember right.
I remember 1 year at lease renewal the owners of a small parcel the poker room was on, would not sign a lease. It was right in the middle of the casino. We joked they would have to fence the poker room off.