History as we've learned it obscures an appropriate view of General Lee's stature in 1775. It is said that when Lee accompanied Washington to Cambridge, Lee was at every town as much an "object of curiousity and admiration" as General Washington. While not broadly written about or remembered today General Lee was a successful military commander and politician, and as much a celebrity as any military figure of his time.
General Lee's first headquarters was the Royal Mansion in Medford. Lee called the building "Hobgoblin Hall" after the echoes that filled the halls with every slightest sound. In 1775 Washington asked a committee of Congress to find more suitable housing for General Lee. The Oliver Tufts House was at this time unoccupied, was closer to his troops, and had a view clear down to the harbor. Thus General Lee moved his headquarters to this house.
The map included at right shows some of the nearby military fortifications of the revolution. The fortification at Prospect Hill and the location of the French Redoubt are well known. Writings from the time mention a "White House" redoubt about which less is known (and which is not shown on this map). One theory is that this redoubt was so called because of its proximity to a white house ... the most logical candidate being the Oliver Tufts house which was immediately to its rear. It is not known that the house was painted white at this time but it likely was so.
That said, perhaps one of the most convincing references is one that speaks in a more general sense: “Tradition also has it that Washington frequented or visited certain houses within Somerville territory. He must have. That he did not, would be almost inconceivable. Several of his generals were quartered here. He must have stopped at their headquarters on his tours of inspection for purposes of consultation, shelter, rest and refreshment. Even if those reasons did not compel such visites, the most ordinary dictates of courtesy to his staff, and considerations of the military morale of the leaders, would make such measures of paramount necessity. …. “