No padding; however, because the planar format implies 8 horizontal pixels in a byte, all bitmaps will naturally need to have a width that's a multiple of 8 pixels. This means you'd need to pad out any bitmaps with non-conforming widths (either as a requirement on the user, or do it in the program).
Actually, I just remember something: I believe at some point when I was writing myvgaspec.exe, I toyed with the idea (because Lemmix didn't exist at the time, and LemEdit doesn't support VGASPEC levels) of making VGASPEC levels viewable in LemEdit via a custom VGAGRx, where the "terrain pieces" are basically just the whole 960x160 VGASPEC bitmap carved out into 60 64x40 bitmaps in a 15x4 grid. Position the terrain pieces correspondingly in the LVL data, and you can view and edit your VGASPEC level in LemEdit!
This idea soon became obsolete with the emergence of Lemmix (which finally allows proper viewing and editing of VGASPEC levels), but one thing I remember out of that attempt was that the VGAGRx file (compressed) needs to be below a certain size, or you'll get strange graphical glitches in CustLemm/DOS Lemmings. It's not clear what that maximize size is. The point is that you want a really good compression algorithm on the VGAGRx data, though fortunately I think Mindless's tool for compression is excellent in that regard.