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.
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.