Why can't I use lithium batteries in this multimeter?
Let's look at the data sheets here.

Lithium:
http://data.energizer.com/pdfs/l522.pdf



Standard:
http://data.energizer.com/pdfs/522.pdf



My guess is we can probably use the 20-33 mA curves for each (the "toy" curve). They look roughly the same in terms of what voltages are outputted (lithium is just way more flat). Based off of this, you should be fine. The only thing of note is that your "low-batt" won't work quite right (it'll probably kick in at around 6.5V or so, which you'll see for 5 minutes before it keels over).