Haven't be able to find out anything else which, with so much information, is frustrating.
I wonder how much of the information can be relied upon though. William Halsey must have been a terrible state, so it wouldn't be surprising if he had made a mistake with the names. Also, the type of person Lucy seems to have been, how many of her 'husbands' did she really marry.
Checking the High St Bordesley address for the rest of the 1930s is the only thing I can think of atm but that may have to be at the library.