The transmitted headword is third person singular, present optative passive, of (ostensibly) the verb kai/w "I burn", and as such might have been extracted from (e.g.) Pausanias 1.30.2, on Athenian torch-relay races. However, the gloss is nonsensical for this verb, and other lexica (see the references in Photius kappa574 Theodoridis) give the headword as ke/oito, which was pronounced the same in Byzantine times and is the corresponding optative of kei=mai. If ke/oito is correct, its source might be e.g. Herodotus 1.67.3, Isaeus 6.32, Plato Republic 477A or Laws 841B, but there are numerous later possibilities.
It remains uncertain why the gloss has the middle/passive form. The middle is more consistent with the initial sense of the verb u(pa/rxw, "to undertake, to begin at something", than its more common sense "to exist", but it does not seem to fit here.
[Even as it is spelled, the entry is out of alphabetical order, except in ms M where it has been moved to the correct place.]