Possibly this is the song (click on the title).

Title: Horwitz & Bowers' Latest Comic Novelty. Lucky Jim. Mock Ballad.
Composer, Lyricist, Arranger: Words by Chas. Horwitz. Music by Fredrick V. Bowers.
Publication: New York : M. Witmark & Sons
Date: 1896
Form of Composition: strophic with chorus
Instrumentation: piano and voice
First Line: Jim and I as children played together
First Line of Chorus: Ah! lucky Jim, how I envy him
Advertisement: ads on inside back and on back covers for M. Witmark & Sons stock
Subjects: Friendship; Spouses; Widows; Death