Yes, lunchbox is a common noun, a Word for any lunchbox of any kind.
A proper noun is the name of a specific person, place, thing, or a title; for example:
- Connie Henninger Neiman, The Lunchbox Lady, Baltimore, MD
- West Lunchbox Street, Kuna, ID
- The Lunchbox (restaurant), Tallahassee, FL
- Universal Lunch Box with Vacuum Bottle No. 410 (1918 advertisement for Landers Frary Clark Products)
- "The Lunchbox Thief", a novel by Nicole Brown
