A number of us have checked & double-checked the 1939 Register to no avail. I'm a bit puzzled by that 1935 Electoral Roll though as I checked for a Lily Wheeler and nothing came up there. I'll check it again with Talbot Street as an address.
EDIT: The one at the Rising Sun, 35 Talbot Street, appears at that address only in 1935. My next move was to go through the lot again from 1920 to 1960 to see if I could isolate where she came from, but no real luck. The one married to Charles Langford Wheeler first appears with him at 9 Ivetsy Place, Sparkbrook, and is with him at that address until he dies and beyond.
Then from 1939 onwards there is one with a different Charles Wheeler at various back houses in Brearley Street until after the war, but no others. But they appear as husband and wife on the 1939 Register and Lily was born in 1911. They were married in 4 Qtr 1937 and Lily's maiden name was KWEI, so not likely to be that one at the Rising Sun in 1935.
So the Lily Wheeler at the Rising Sun in 1935 is still a possible, but she doesn't appear on the Electoral Rolls previous to this date or afterwards. That seems odd to be suddenly parachuted in and then out!
But on 23 May 1936 the Birmingham Gazette announced its closure along with 7 others:-
There were no other previous adverts for bar staff from 1930 until closure. There is one other possibility with this presumed barmaid. There are numerous other Lily/Lilian Wheelers with two or even three forenames/initials. This could have been one of those, and the landlord, not knowing that she had other names, merely added her to the Electoral Registration form as plain old Lily. There is just no way of knowing.
Maurice