In British usage, a lumber room is a room in a house used primarily for storing unused furniture. British stately homes often had more furniture than could be used at one time, and storing the furniture for future use was more common than selling or discarding it.
The first reference to the phrase "lumber room" in the Oxford English Dictionary is the 1740 novel Pamela. Subsequent references can be found in A Christmas Carol by Charles Dickens, Arthur Conan Doyle's 1891 Sherlock Holmes short story "The Five Orange Pips", and The Fellowship of the Ring by J.R.R. Tolkien. A lumber room is described in detail in Saki's short story "The Lumber Room":
Often and often Nicholas had pictured to himself what the lumber-room might be like, that region that was so carefully sealed from youthful eyes and concerning which no questions were ever answered. It came up to his expectations. In the first place it was large and dimly lit, one high window opening on to the forbidden garden being its only source of illumination. In the second place it was a storehouse of unimagined treasures.
The OED mentions in the verb "lumbering" that it first meant to obstruct with pieces of wood to make things from, and then shifted to general obstruction, hence furniture fit the later meaning[clarification needed].
Therefore I will order my own little chapel, which has not been used for two generations, for any thing but a lumber-room, because our family seldom resided here long together, to be cleared and cleaned, and got ready for the ceremony, if you dislike your own chamber or mine.
Sitting-room, bedroom, lumber-room. All as they should be. Nobody under the table, nobody under the sofa; a small fire in the grate; spoon and basin ready; and the little saucepan of gruel (Scrooge had a cold in his head) upon the hob. Nobody under the bed; nobody in the closet; nobody in his dressing-gown, which was hanging up in a suspicious attitude against the wall. Lumber-room as usual. Old fire-guard, old shoes, two fish-baskets, washing-stand on three legs, and a poker.
There was one singular exception, however, for he had a single room, a lumber room up among the attics, which was invariably locked, and which he would never permit either me or anyone else to enter. With a boy's curiosity I have peeped through the keyhole, but I was never able to see more than such a collection of old trunks and bundles as would be expected in such a room.
PPPS. I hope Butterbur sends this promptly. A worthy man, but his memory is like a lumber-room: thing wanted always buried.