Bait or Bate - Update
I grew up in Accrington and knew when quite young that my dad took bait/bate to work in a box. The contents would be eaten at bat/bait time. Aged 16yrs, I became a clerk at a pit in Burnley and heard colliers talking about their 'snap' - food which they took down t'pit in a 'snap tin'. I learned that in other areas of Lancashire, some colliers and other workmen called their home-packed food 'tommy-bit'. When I later went to live in a Fylde village, a farmer pal introduced me to the term 'bagging' , which covered the food to be eaten at break-time . My police colleagues used the term, 'refs' for the 45-minute break for refreshment and the food taken to work, though there was no use of a term for the receptacle in which it was carried.
Bate (my preferred spelling) will be found in any of the glossaries found in Shakespeare's works as meaning simply 'food', so the word we use in Lancashire comes from general use throughout the country in the 16th century, and likely much earlier. Thus it is a pure dialect word - one which was in everyday use many years ago, but which has 'died' so far as universal use is concerned, but has lived on in pockets of the country such as Lancashire.