Just seen this topic tonight.
The lodge was at various times the mine offices - the gates were just to the right on the photo - and also the undermanager's house. It wasn't ever an engine house (the nearest shaft being No 3 along the path under the candlestick chimmney). One feature of the lodge, now obliterated by the works down there, was the tunnel staircase leading from the basement down to the harbourside level about 60 feet below. At the botom used to stand the Wellington PH - handy for stressed clerks or undermanagers. I haven't been along there since the "improvements" were done but it was possible until this year to see where the engine house (demolished post-war to provide the embankments at Whitehaven RL ground)abutted the retaining wall and the positions of Nos 1 & 2 shafts could be located on the car park. There were also some really interesting features underground at Wellington which I always regret never being able to photograph.
The "cottage" buildings were never connected to mining (except as a place to quench a collier's thirst). They are what is reputed to be the oldest house in Whitehaven and still, amazingly, occupied. It used to be a pub, one of the earliest "Bowling Greens", the remains of that feature still visible to the west side of it. Later on it was a coastguard lookout station the danger signal flown there giving the next use as a pub the name "Red Flag".
Nowadays it is known as "Jonathan Swift House" from the as yet unproven theory that this was the house where he spent some of his childhood years, the distant view of people on the harbourside giving him the idea for Gulliver's travels.
The building at Redness point was associated with the Lonsdale Ironworks which occupied the area between the railway and cliffs north of William.