How do you determine the black/white cutoff exposure for lith film?

I have to preface this by saying that lith film is almost exclusively used where paper would be, as something another image is printed upon (except, I assume, in some types of process photography), so there would be very few "straight" photographers who would be able to give you an answer that relates to EVs and rated sensitivity. Whether we're talking about enlarger projections or contact prints, it's much more a matter of test strips than of measured exposures. Keep in mind that we mostly used tungsten light sources, and that lith film is usually orthochromatic (you can work under fairly bright red safe light and use rubylith film for masking), so measuring the total light hitting the film would have told us little about the actinic (shorter wavelength, more energetic) light content of what we were measuring. (Just as an aside, orthochromatic response isn't "added for easier handling in the darkroom" as much as it is to remove the necessity of going outside and exposing the film to sunlight or sparking up an arc lamp. Deciding to leave it at ortho rather than going all the way to pan makes darkroom life easier, yes, but the film would naturally only be significantly sensitive to the high end of the blue spectrum.)

Lith film doesn't so much have a "breakover" as "levels of contagion". That, in fact, is how it is used to create halftone images: the grey-scale image is projected onto the lith film through a uniform screen, and the width of the resulting lines (or the size of the dots) is determined by the lith film's exposure to light. Low exposures are "less contagious", so only small areas of the film will precipitate silver when developed. High exposures are "more contagious", and the reaction can actually extend significantly beyond the exposed area of film. Coninuous areas of black in a halftone are the result of this contagion extending to the area between the dots. Anything above the film-base-plus-fog exposure will result in some high-density silver when developed, but the size of the silver areas will be determined by the exposure. That means that trying to create images from unmasked continuous-tone sources (whether from a negative or from direct exposure to a scene through a camera) is going to result in blotchiness with only a very little control.

If there is sufficient contrast (as with a photogram), you can get a good one-step black-and-white image (not greyscale). But when trying to posterize a continuous-tone image into black and white without a screen, you pretty much have to severely underexpose anything you want to remain white and aggressively develop everything else to black. That, in turn, means that Zone I, or even Zone 0 "plus a little bit" would be the breakover point, I suppose (if you take it as read that Zone 0 is film-base-plus-fog), and you'd need to place your blacks at Zone 0. But you'd need to meter that with a red-blocking filter, and I have absolutely no idea how you'd determine N, since there are really only Zones 0 and X to work with, plus a bit of bleed between them.