Interesting that that sketch of the Lamb House shows gables that weren't present at its demolition in 1886, nor going back as far as the 1835 sketch of post #422.
The Birmingham Daily Mail article "Destruction of the Oldest House in Birmingham" (18th May 1886) recounts that the building was to be stripped back to its original timbers for inspection and recording before being pulled down.
Perhaps the sketch above was part of that recording process and the author,
Jethro Cossins (1830-1917), being an architect, was extrapolating the building's original construction from what the timbers revealed.
The Mail piece quotes a 1772 description of the vicinity (the "Welch End" neighbourhood) showing that the name "Lamb House" goes back at least that far, considerably pre-dating the time that my Allday relatives sold (and raised?) their "house lamb" from the premises in the 1820s. Prior to that, the house is claimed to have been the "Fox and Dogs", suggesting it was a public house.
(For those with access the Mail article is on the British Newspaper Archive)