This is a very good question.
Some connection with Greenwich Hospital, London Lead Company suggests itself, except that Hospital level was driven about 1864 when John Barratt was running the mines.
The area was worked originally by German miners and afterwards acquired by Royal Mines Copper which is associated with LLC, but we talking nearly 200 years earlier!
I actually love these sort of questions and eagerly await the answer to the riddle.
My avatar is a poor likeness.