Exegesis:

kai basileusei epi ton oikon Iakōb ‘and he will rule over the house of Jacob’; the subject changes abruptly from God in the preceding clause to Jesus.

basileuō ‘be king,’ ‘rule,’ in Luke always with epi followed by an accusative to indicate the king’s subjects.

oikon Iakōb lit. ‘the house of Jacob,’ i.e. ‘the descendants of Jacob,’ cf. on v. 27.

eis tous aiōnas lit. ‘into the ages,’ hence ‘for ever.’

aiōn ‘age.’

kai tēs basileias autou ouk estai telos lit., ‘and of his reign there will be no end.’ The place of the genitive tēs basileias at the beginning of the clause represents an attempt to carry over the dominating idea of the preceding clause (basileusei) into this clause.

basileia ‘kingship,’ ‘kingdom’ or ‘reign,’ ‘rule.’

Translation:

The verse is consecutive to v. 32b; hence and may be rendered, ‘then,’ ‘thus,’ ‘and so’ (Navajo). The two clauses parallel each other, the second semantically repeating the first and thus reinforcing it.

The reference of he may have to be specified, e.g. by qualifying the pronoun by means of a deictic element, or by substituting ‘your son,’ or, ‘Jesus.’

Reign over, or, ‘rule,’ ‘be king/chief over,’ ‘have power/authority over,’ ‘command,’ ‘hold’ (Ekari, cf. on “king” in 1.5).

House of Jacob refers to a group that is coextensive with the people Israel, whereas “house of David” in v. 27 refers to the royal clan; accordingly “house” may have to be rendered differently here, e.g. by ‘people/tribe’ (Tae’), ‘all-the-progeny’ (Balinese, instead of ‘descendants’ in v. 27).

For ever, or, ‘age after age’ (Marathi), reduplication of ‘age’ (Telugu), reduplication of ‘what-day/when’ (Tamil), ‘in-long-length(-of-time)’ (Malay and Batak Toba); or a negative phrase, e.g. ‘without an end(ing)’ (Tboli).

Of his kingdom there will be no end, or, ‘the length of his being-king will be without limit’ (Balinese), ‘he will never stop commanding’ (South Bolivian Quechua), ‘his chieftainship will not finish’ (Tae’), ‘his reign will not come to a stopping place’ (Chokwe). For Kingdom (also in 4.5; 11.2, 17f; 12.31f; 21.10;22.29f) see on “king” in 1.5 and on “kingdom of God” in 4.43. If this noun has to be rendered by a verb, e.g. ‘he will rule (as king)’ and/or if “forever” in the preceding clause has to be rendered by a negative phrase, e.g. ‘without end,’ the two clauses may come to resemble each other too closely. In order to avoid repetition then the translator may try lexical differentiation, e.g. by the use of synonyms, such as ‘exercise authority’ after ‘hold/rule’ (Ekari), ‘be chieftain’ after ‘have-as-subjects’ (cf. Tae’ 1933), and/or, ‘without limit,’ ‘unrestricted’ after ‘without end’; or he may try to turn repetition to advantage, and say in the second clause something like, ‘indeed, reign without end he will,’ cf. also the Sranan Tongo rendering of this verse, ‘he will be king over…, he will remain king….’

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.