There remains different opinions about when you should install new cells. When voltage drops to a certain level the halogen cycle becomes inactive. However, lower voltage boils off less tungsten from the filament. From what I know at this time, I think it's a wash - that it won't affect lamp life to use weak batteries. Perhaps some lamps are constructed differently and darken the globe less when running hotter on fresh cells. Whether that also extends their life is debatable.
No two cells have equal capacity, which is why it's not good to use a rechargeable light until it's very dim. One or more cells could be reverse charged by the stronger ones. Likewise, primary cells will vary in capacity and often one will die before the other. Sometimes, though, lithium cells will die, unexpectedly, while in storage, well before they normally should have. This may be due to the highly active nature of the lithium, where a minor manufacturing defect has more serious consequences than, say, in an alkaline cell.
These are just my guesses, others may have more accurate information.