Rechargeable 1.5V lithium batteries are complicated animals. Not a battery, as such, so don't rely on standard battery chemistry descriptions to cover them.
From tested behaviour:
There's a real 3.7V lithium cell inside there somewhere, with a charging voltage of over 4V on the battery terminals.Open circuit when charge is terminated internally. When it's not being charged, a switching regulator takes over to produce 1.5V on the same terminals, drawing from the lithium cell. This buck regulator is unstable when the battery is not being used, so the battery terminal voltage jumps around if you try to simply measure it. I wonder what this does to devices that count on the low noise usually produced by simpler standard cells. Guess I'll find out the hard way. Loaded, the voltage will stabilize, but then you've got normal switching ripple and, supposedly, emc issues. Nothing in the literature (?)- it's still the wild west as far as battery products go, in the far east. Currently less than US$1.50 per in low volume retail.
I lucked into a bunch of rechargeable 9V (PP3) lithiums the other day - furnished with a micro-usb port for charging. Same basic idea, but with a boost regulator supplying the terminal voltage.
RL