Does the DigiSnap 2100 run off the large lithium battery as well or is it run from it's small internal battery? If it is from the small battery, should I replace it with a lithium battery if I want to be assured it is not going to run out over the period of many months?

The large Lithium-Ion Polymer battery will power everything!

If you've installed an internal AAA battery for configuring the DigISnap away from the housing, please remove it when using it in the housing. The external power will 'fight' with the battery, and end up making a mess.

By the way, the DigiSnap will save all of it's configuration changes indefinitely, even without power applied... you don't need the internal battery to keep the settings.

The camera however is a different story. There should be batteries installed in the camera, simply to keep it's internal clock and calendar going when the external power supply is not active.