Exegesis:

kai elegen ‘and he said’ or “he also said” (New English Bible), preferably the former, see below.

kurios estin tou sabbatou ho huios tou anthrōpou ‘lord of the sabbath is the Son of man,’ i.e. if already David was exempted from the law, so much more the Son of man, which Jesus implicitly claims to be. The clause represents more a conclusion from what precedes than an addition to it. kurios ‘lord,’ or ‘master’ with emphasis at the opening of the clause. For huios tou anthrōpou cf. on 5.24.

Translation:

Is lord of the sabbath implies authority (for which cf. on 4.32) over the rules about the observance of the sabbath. Some possible renderings are, ‘exercises-power-over’ (Sundanese), ‘rules.’ In Batak Toba idiom requires another sentence structure, i.e. ‘the sabbath conforms to (or, is dependent on, lit. (has) a teacher/master in) the Son of man.’ Formal identity or relationship of the expression used here with the term for ‘Lord,’ when occurring as a Messianic title, is not of primary importance.

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.