If they are the only source of illumination, they'll be eating in the dark. I'd need to know the specific LED used and have a proper datasheet for it to make a good approximation of lumen output at drive current (with a CR2032 or whatever you settle for, IMO CR2032 is only enough for decoration purposes, not area lighting), but even with multi-chip 10mm LEDs (which will need PCB heatsinking for reasonable life - running just one night, I couldn't guess if they'd last or burn out w/o heatsinking), you'd probably end up under 10 lumens per LED, and definitely so powered by 1 x CR2032 which just can't sustain the necessary current.
As BobK already explained, MCD is just intensity, determined by the shape of the plastic lens molded into the LED casing. Even 120' would be rather narrow for a traditional lantern shape. In theory you might be able to use a belt sander and sand down the lens dome on an LED (or buy some with flat ends), then polish to near optically clear to get a beam closer to 180', but in practice that would be a pain in the *** to do for more than a small # of LEDs.
For this reason I would go with bare chip LEDs instead, then under-driven enough they won't need a heatsink.
If they are the only illumination, everyone has their own ideas about what is bright enough to eat but I'd think you're going to want (very) roughly 100 lumens per square meter, or even a lot more if the light is cast evenly around lanterns so it is going everywhere instead of just directed down at a table.
It seems very impractical, I think I would consider a single battery pack with much higher capacity cells then run wire between all the lanterns, maybe use a deep cycle 12V marine battery. LEDs are comparatively efficient but it still takes a fair amount of current to light up an area for more than a few minutes, yet you didn't mention the amount of area.
