This verb clearly derives from an Arabic word still used in its own right in Algerian Arabic: kun كون "be", with regular assimilation of n+l to ll and reinterpretation of the root. waš y-kul-lek واش يكوللك "what relation is he to you?" was originally waš y-kun-lek واش يكونلك "what is he to you?" But that construction seems rather odd and unidiomatic from a Classical Arabic perspective. You don't normally use an equational verb "to be" in the indicative present tense like that, in Classical Arabic or even in Algerian Arabic; you would rather expect something with a pronoun, like *wašen huwwa lik واشن هو ليك (which you don't hear). What's going on here?
Flipping through Dallet's (1982) enormous dictionary of Kabyle as spoken by the Ait Menguellet, I came across the answer. The Kabyle verb ili "to be" (imperfective ttili) matches Arabic kun كون fairly well in its usage. In the imperfective, with the dative, it means "be related to" (his gloss: "être parent avec, avoir relation de parenté à"): d acu i-m tettili? "what relation is she to you?") It likewise has a reciprocal myili (imperfective ttemyili) "have in common; be related to each other", which in the latter sense only seems to show up in the imperfective: nettemyili "we're related to each other".
It seems clear that the Algerian Arabic verb derives from an excessively literal translation - a calque - of the Kabyle expression, probably by people whose first language was Kabyle. But since then it's taken its own path; whereas in Kabyle the meaning "be related to" remains a context-specific sense of the verb "be", in Algerian Arabic the change of n to l has allowed it to become an independent lexeme in its own right with no one-to-one Kabyle translation equivalent. Contact catalyses change, but the resulting change follows its own path.