Crontab offers many refined facilities for Western calendaring, but none for traditional Eastern-- lunar-- designations. So for example, if one wants specify regular occurring events on full moons or on new moons, there is no way to do this. Emacs (a text processor!?) accomplishes this. The math for calculating lunar calendaring is already available; mathematical functions are already available for simple downloading and so would need simply integration into crond.
User settings in crontab would make most sense designated in the 'day of month' field with keyword either 'full' or 'new' (abbreviated with 'f' or 'n') prepended to a signed integer number of days (N * 24 hours). I.e., "new+5" would specify '5 days after the new moon'; "full-1" would specify "24 hours prior to the full moon"; "new+0", "new-0" and "new" would all mean the same: "the moment of the new moon".
I suppose that alternate syntaxes could be more refined, including hours and minutes before/after new/full, so possibly useful, but then also more complex. Alternate and more refined time periods would be a question for developers.