Exegesis:

sēmeron sōtēria tō oikō toutō egeneto ‘today salvation has come (lit. has happened) to this house.’ For sēmeron cf. on v. 5. For sōtēria cf. on 1.77. It is best understood as consisting of forgiveness of sins. oikos is used here in the meaning ‘family.’

kathoti kai autos huios Abraam estin ‘since he also is a son of Abraham.’ kathoti (cf. on 1.7) introduces a clause that states grounds which are supposed to be known. autos refers emphatically to Zacchaeus in the third person, notwithstanding the fact that, strictly speaking, Zacchaeus is addressed by Jesus. This implies that the causal clause is spoken also for the benefit of those present. For huios tou Abraam cf. on 13.16.

Translation:

Salvation has come to this house, or, ‘has been given to this house’ (cf. Nieuwe Vertaling), ‘this house has received salvation’ (Sranan Tongo); or, where a shift to a passive or active verbal construction is required, ‘this house has been saved, or, has received the one who saves it.’ House has been rendered “household” (The Four Gospels – a New Translation), ‘the-whole-family’ (Balinese), ‘all-who-are-in the house’ (Bahasa Indonesia).

Since, cf. on “inasmuch” in 1.1.

He also. Where a third person reference to the person addressed is unacceptable one may shift to the second person (as in Tzeltal), or change the introductory words into, ‘thereupon Jesus said,’ or, ‘Jesus replied to this.’

Is a son of Abraham, or, ‘is one of (or, belongs to) the sons/descendants of Abraham.’

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.