I think there are instrument drivers for the LeCroy scopes, and those instrument drivers use VISA. The port number is determined by the instrument vendor. I'm not sure if the LeCroy manuals tell you what that port number is, but I'm sure that's what the instrument driver uses.
And your last instinct is right; this is definitely not what remote VISA is for. That's for one PC using instruments connected to another PC, for example. Dan Mondrik National Instruments
