This marking has me a bit confused, I have not seen the Roman Numerals with a point after them as in B.A.I., but I agree that it is not an L, as there should be a point after a letter. B.A.I would be East Prussian, but did the Bavarian B.A.s use the point to differinciate themselves, i.e., does the B.A.I. mean Southern Bavaria?
Gus