No one knows what significance, if any, it might have. They could have just incremented to 04D. 04L appears about the same time as 05A, they were interspersed in production over a period of about 2 days. A few Firebirds were 04L. The 'broken die' theory seems far-fetched.
The body tag was only referenced by Fisher Body-Norwood assembly had no use for it. Fisher could have used 04L to signify a number of situations: a different process, orders to be expedited or delayed. I have compared the 60 or so 04L cars in the db and nothing jumps out. Maybe slightly odd, none are 6 cylinder.
Or, it was just an error and has no special meaning.