Most boxes I have of cartridges with a lot number on the case, this is the lot number of the case, not the loaded round. In all cases, as best I can remember, the lot number on the case usually does not match that of the lot number on the box which indicates the load lot (and sometimes date when the loading was done) unless by hapenstance-like lot 1 of 1944 cases may have been used for loading Lot 1 of 1944 ammunition. German WWII ammo almost always lists the production lot of the case, powder, primer bullet and sometimes bullet core and seperately, above all this data is the load lot. There are examples when the case was manufactured a year or more, sometimes a number of years, before the ammunition was actually loaded. A good example is the green case Nahpartonen 9mm P08 cartridges. All cases are headstamped aux St+ 33 42, but the lots are Lot 1 and 2 of 42 (as I recall), but there are boxes where the load was from 1943. During WWI the “lot” number was actually the month of the year, and it is pretty common to see cases with two or even three different months all packed in the same box (with the load lot indicated on the label. I have found similar things on other than German boxes, but the Germans put so much information on their labels that they make most of the good examples. In fact some of the labels indicate that the cases (or other components) are from various lots/dates. In fact there is an ak label from 44 indicating that the cases could be from 42, 43 or 44.
This is not unusual and happens in US commercial ammo also. There is a known box (all I have is the photo) full of UMC headstamped HP cartridges, but the box label is REM-UMC in a style from the 1918 time frame. There are WRACo 9mm hsts which are prewar production, loaded with wartime/post war bullets in boxes with load dates of 1948!
Never assume the lot number and date on a case tells you anything about when the ammo was loaded, except that it was not loaded before the date on the case-and then this is only true if they really are legit lot/dates, and examples where false dates/lots have been put on cases have been discussed before on the Forum.
PS: In 9mm P08 ammunition from WWII, lot 1 cases seem very hard to find. In many manufacturers and years, I have all or most of the lots up to the highest known lot numbers, but lack lot 1. I have wondered if the first lot of the year was often small and used for qualification or validation testing rather than for operational production. If someone has thoughts on this please open a seperate thread for the discussion. When I get back home I can do a quick check of the manufacturers and years I lack lot 1 and see if it is just me!