Ah, that's interesting, for the 'S' date letter, with larger serifs, was also used in 1836, so that is much more likely to be the correct date.
As to whether Lee was still working at that time, I'm unsure, perhaps another member has some knowledge of him. The engraving would have been nothing to do with the assay office, so if the maker was Liverpool based, then it's likely to have been done there, either by the silversmith himself, or by a specialist engraver.
The 'head' mark is the Duty mark, it was applied at the assay office along with the other hallmarks after the Duty had been received from whoever submitted the silver for assay.
See Duty mark at: http://www.925-1000.com/silverglossary2.html