Etymology
From earlier lunching, of uncertain origin.
Possibly derived from an earlier *lumpchin, *lumpchen, a diminutive of lump (“chunk, parcel of food, lunch”), thus related to lunch, q.v. It is unclear which came first: whether lunch is a shortening of luncheon, or whether luncheon is an augmentation of lunch. Possibly influenced by nuncheon (“light snack taken in the afternoon”).
The "sausage" sense is probably a shortening of luncheon sausage or luncheon meat.