just to add my 2 cents worth from the lands down under...
note: we use the term ACTIVE for 'hot' here (both in NZ and across the ditch in Australia), but i will use the term HOT so as to not confuse things further. we also have NEUTRAL connected to GROUND via a single link at the distribution board.
1. a cardinal rule of mains wiring (here in NZ) is that swapping HOT and NEUTRAL should never create an unsafe situation. if any piece of equipment were to contain an internal connection between EARTH and NEUTRAL, that would violate this rule if said equipment were plugged into an outlet with HOT and NEUTRAL reversed.
2. with the one exception of double-insulated equipment, all exposed metal parts must be connected to EARTH. this ensures that you can not receive an electric shock via contacting said metal parts.
the above are enshrined in law.
applying the above two rules, (a) your isolating transformer should have the metal core along with any metal casing components connected to EARTH. and (b) the incoming HOT and NEUTRAL must be kept isolated from EARTH. if these conditions are not met, the equipment has the potential to create a hazard, as well as being illegal.
as for the secondary, well the terms L1 and L2 are an apt choice here, indicating the secondary 'knows' nothing about HOT and NEUTRAL. L1 and L2 are not a part of the mains supply system, however do need to be treated with care as a hazardous voltage exists between them.
EARTH, while advisable to be connection to the DUT, is optional as your isolating transformer creates a safety barrier. while current can flow between L1 and L2, it can not flow from the DUT down the EARTH wire.
having said this, there is no sensible reason to connect either L1 or L2 to EARTH that i can think of, as there is simply no path for the secondary current to flow through apart from between L1 and L2. as others have said, with L1 and L2 kept floating, you are free to work on 'live chassis' equipment with that chassis connected to the same EARTH as your oscilloscope or other expensive/fragile equipment. said 'fragile equipment' includes the service-person!
cheers,
rob :-)