While family tradition holds that this chair descended in the Lambert family, it appears to be from the same set as the chair in plate 163 of William Horner's Blue Book of Philadelphia Furniture and also advertised by David Stockwell in Antiques Magazine, January 1948. That set of chairs has a reputed history in the Custis and Lewis families, and is thought to have occupied President Washington's drawing room at his High Street residence in Philadelphia, from 1790-1796, while Philadelphia was the nation's capital.
This chair is very similar to many carved by James Gillingham and Thomas Tufft. See for example Joseph Downs, American Furniture: Queen Anne and Chippendale Periods (Winterthur, 1952), figures 134 and 139. Like this chair, these examples display similar Gothic-pattern splats, C-scroll carving on the apron, C-scroll cabriole legs with lightly carved knees and ball-and-claw feet.