Hmm, I just look more closely at the file listing screenshot you posted above, and noticed some inconsistencies.
First of all, why are most of the files shown with the Windows Media Player icon? .DAT files shouldn't be something that Windows Media Player would handle. But anyway, let's ignore that for now, since you said LemEdit does work, so maybe it's just Windows Media Player not being correctly set up. That shouldn't affect us.
Second and more importantly, I noticed that your levelpak.dat file is shown in the screenshot as "levelpak.dat". Notice that, even though there are other .DAT files like VGAGR0.dat or ADLIB.dat, they are simply listed as "VGAGR0" and "ADLIB", without the ending .dat. This makes me suspect that you somehow got your levelpak file named as "levelpak.dat.dat", and Windows, when displaying the files, just uniformly truncated the .dat off all the files being displayed, but since levepak.dat.dat has two ".dat" you still see the other one.
To confirm, try this: in DOSBox, go to the LemEdit directory, then type
dir lev*.*
and see what gets shown. It should list levelpak.dat. If you don't see levelpak.dat being listed, then you misnamed the file. Go back to Windows and change it so in Windows it is shown as "levelpak", without the .DAT. Then do the command above in DOSBox again to confirm that the name is correct.