Q: Can you use lithium-ion batteries instead of NiMH?
A: No. Electronic gadgets are manufactured to be able to use only a certain size of battery - AA, AAA, or the Various sizes of Lithium-ion batteries. Rarely does a gadget allow two sizes. Old Kodak P&S cameras has these feature but they use obsolete battery sizes. There are no Lithium-ion batteries the size of AA or AAA. They always come in rectangular shapes and are specifically made for a narrow range of gadgets. They also have 3.7 volts per cell. So if ever a miracle happens and someone makes a Lithium-ion cell the size of a standard alkaline, the voltage would probably damage your gadget.
If you want, you can use Lithium batteries. These are different from Lithium-ion batteries which hold up to 6 times the charge of NiMH, they give 1.5v per cell and has minimal self-discharge rates. The down part is they are not rechargeable.
If you want to recharge alkaline batteries, I have some instructions here: How to Recharge an Alkaline Battery