Laces and Graces is an American two-step sequence dance described by seminal American folk dance collector, teacher, caller, and historian Lloyd Shaw in his invaluable work, The Round Dance Book (1948). Shaw gives no specific date for Laces and Graces, so the best I can suggest is early 1940s. It does not appear in Shaw's earlier work, Cowboy Dances (1939).
Laces and Graces is easy for anyone who knows two-step and, importantly, has available music, including both sheet music and the very recording cited by Shaw in 1948.
Shaw called Laces and Graces a "dance built to fit an old-time piece of popular music", but didn't say anything else about the music, which was originally composed by Gustav(e) Salzer and John W. Bratton and published in 1903.
Out in Oregon, the Polk County Observer made note of the new hit in a short article entitled "Popular New Music" on November 27, 1903:
"Laces and Graces," an instrumental novelty by Gustav Salzer and John W. Bratton, is just what its title would suggest its being; that is, a dainty, graceful melody, full of the atmosphere of the ball room and reminiscent of frills and flirtations. It is a companion piece to Mr. Bratton's "In Cozy Corner," and while it has none of tho odd little twists and turns of its famous predecessor, it yet possesses an originality and charm which is already making it a great "go," although it has only been out a few months. The title page of this composition, gotten up by the house of M. Witmark & Sons, in the most artistic manner, represents a white lace handkerchief upon a dark back ground, and the design, though simple, is so remarkably striking that it is already a prominent feature of the window displays of most of the prominent dealers.
A scan of the original article may be found at Historic Oregon Newspapers. "Popular New Music" starts about a third of the way down the third column from the left. Part of the same text had appeared in the Democrat and Chronicle of Rochester, New York, on November 15, 1903 (here), suggesting that it was at least partly copied from some major newspaper or syndicated piece. A little digging turned up a copy of the original sheet music at the Parlor Salon Sheet Music Collection at the University of Maine, from which the image above, complete with its charmingly irrelevant picture of pseudo-1830s dancers practicing their steps, is taken. The lace handkerchief suggests that "laces" refers to lace in the sense of trim or fabric, not to shoelaces or corset laces.