I use the 4LR44 battery from eBay. I buy the ones for doggie shock collars. Way cheaper than the lithium ones. Don't know of the cheap batteries last as long though, but good enough for me.
For the RZ67 and the RZ67 Pro II, the battery specifications in the manuals did not include lithium batteries. It may be that before the Pro IID, the website specifications recommended against them.
With the Pro IID, lithium batteries are recommended in the manual (actually in two different places). It may be, however, that when the website specifications were changed to list the Pro IID instead, that part wasn't updated.