Best way to check for a "G" on return leg???

I can see there are several ways of checking for G availability on the reward fares/upgrades pages of the VAA site (I have an "S" PE ticket for the return leg of an LHR-LAX-LHR trip in June (out on 6/6 and returning 11/6 - I've got a G on the way out y) but so far nothing doing on the return leg :# ), so......

1) Should I put in one-way LAX-LHR leg and see what that brings up, or
2) I could try LHR-LAX-LHR and see what availability that shows etc.

But if I put in LHR-LAX-LHR will it show that there is "nothing available" if only ONE of the 2 legs has no G fares, LHR-LAX for example, and therefore I'm not made aware of a G on the LAX-LHR leg - in which case I would have called VAA and booked it.

Is it better to just enter the one-way LAX-LHR return leg to see if G's are available, or am I better putting in the whole trip ?| ???

Thanks.

Flights from the US back to the UK are notoriously harder to find Gs for.

I'd try both just in case, as there does seem to be anecdotal evidence suggesting Gs sometimes show up for journeys originating in the UK but not on the same flight originating in the US.

Even if no more Gs are available for your outbound flight, it should bring up the calendar showing when they are available.