The two most likley lodges that I can find from the 1923 lists are:
Lodge number 2 - Queens Head, York St, Stepney (met on a Wed). This was a very old lodge, probably formed in the early 1780's
Lodge Number 434 - Ship Afloat Lodge, Spread eagle, Gill St. Limehouse (met on a Tue)
Both Lodges have long gone I am afraid but ther may be something lurking in a local library/record office. If you find anything please let me know.
Regards
Barry