Sweet and lovely would have been recorded by a number of artistes: each record label used to release its own version of a popular song with their own singer; so there would a Columbia one, a Regal one, A Rex one and so on. My 78 is on the Columbia label, performed by the Savoy Hotel Orpheans (Columbia CB376) and this predates the crediting of Carroll Gibbons but by 1931 he was their conductor. I also have it on a CD where it is the version recorded by Russ Columbo; Bing Crosby also recorded a version later in 1931 which was also a hit.
So by 1939 when First of ... is set, the record would be well known and probably considered a standard.