Netto (either Billund or Odense) close at 22:00 and Lidl (Odense) closes at 21:00 so shopping on arrival at Billund will be marginal if you intend to arrive there at 21:00. I suggest you do your shopping with a stop at Odense, there are both Netto and Lidl close to the motorway if you want to get it over with quickly.

The Bilka in Odense (slightly off the motorway) says it's open 06:00-00:00 but that the "bistro" is open to 20:00, the "Carl's JR" (burger bar) to 21:00, and closed on (religious) holidays ("helligdage"). That's a much bigger shop than a Lidl.

There's also a services with a Monarch restaurant slightly west of Odense that might serve you - which closes at 22:00. It might be reasonable to go to the Bilka first and if this fails to provide a restaurant for some reason buy food there and proceed to the Monarch services.