Lithium batteries are occasionally marked 3.6 or 3.7 volts. More often 3.7 because it looks better. But it's a nominal marking and, as said, the real voltage goes from 4.2 (cutoff to prevent overcharge damage) to somewhere around 3 (cutoff to prevent deep discharge damage). So nickel (or alkaline) and lithium batteries will spend a lot of time in the same range, as it were.
It should just work, presuming you take care of charging correctly. There may be a difference in how the battery (and the device!) behaves once the batteries are getting close to empty and how they age. I suppose this is a digital camera that will write to flash memory. That takes a certain voltage at some current. If the battery is too weak and dips when its loaded, the write might get interrupted with undefined results. But it all depends.
If the device and its functioning is very important (you're taking the photo of a lifetime...) I wouldn't risk adding random variables like batteries it wasn't designed for. If it's for random use and will work better for you with the new batteries, I'd absolutely go for it.