So long as you're consistent about how you file records from bands named after 18th century French plays, it doesn't matter too much. Personally I'd file it under D, but can see where if someone thought the band was from Los Angeles, it would be filed under L.
The type of person who would buy a La Dispute double LP (aka me) is not going to look for it in the D section. Luckily the record store did put it under L. Since it's not meaning "The" I'd say that's where it belongs.
They are from Grand Rapids, Michigan.