IIRC, from *my* youth, they were about 1/4" diameter for a D cell. I don't know if I ever bothered with a C cell, since nothing that I had at the time used those. The No. 6 cells (with either thumbnuts or Faheinstock Clips for terminals) were something closer to maybe 3/4" diameter IIRC. I never needed to measure them for my purposes at the time, so this is only from memory which may be distorted as I've gotten larger since them, so my memory of size may be off too.
BTW Various pump bottles of soft soap can be used to distribute WayLube in reasonable doses for cleaning and re-lubing the lathe's ways.
They can also be used to distribute cutting lubes at need if you don't have a constant flow pump to do it.
And *don't* ask me for dimensions. Each maker of the soft soap uses different size bottles, and changes sizes at a whim. The same for dishwashing detergent bottles.
Enjoy, DoN.