1

The word is not found in BDAG because it is only used in the OT, not in the NT.However, this is what the other Lexicons have:

https://logeion.uchicago.edu/κτάομαι

[Isa 1:3 LXX] (3) ἔγνω βοῦς τὸν κτησάμενον καὶ ὄνος τὴν φάτνην τοῦ κυρίου αὐτοῦ Ισραηλ δέ με οὐκ ἔγνω καὶ ὁ λαός με οὐ συνῆκεν

[Isa 1:3 ESV] (3) The ox knows its owner, and the donkey its master's crib, but Israel does not know, my people do not understand."

2

κτησάμενον is a participle conjugated (in the aorist tense, middle voice) from the verb κτάομαι. The verb κτάομαι does indeed occur in the Greek New Testament,1 and it is also found in BDAG.2 It is the perfect tense conjugation of κτάομαι (as noted later in this answer by Wilke/Thayer) that does not occur in the Greek NT.

According to LSJ on the verb κτάομαι,3

LSJ, p. 1001, I., 1.

also,

LSJ, p. 1001, κτάομαι, II., 2.

Granted, κτησάμενον is conjugated in the aorist tense, while κεκτημένος is conjugated in the perfect tense.4 Nevertheless, it seems like a suitable translation of the Hebrew word קֹנֵהוּ (konehu).5

According to Wilke (trans. Thayer),6

Thayer, κτάομαι, p.363


Footnotes

1 Matt. 10:9; Luke 18:12, 21:19; Acts 1:18, 8:20, 22:28; 1 Thes. 4:4
2 BDAG, p. 572
3 LSJ, p. 1001
4 According to Rahlfs’ ed. of the LXX, there are no textual variants for Isa. 1:3.
5 conjugated from the verb קָנָה (kana)
6 Wilke (trans. Thayer), p. 363

References

Arndt, William; Bauer, Walter; Danker, Frederick William. A Greek-English Lexicon of the New Testament and Other Early Christian Literature. 3rd ed. Chicago: U of Chicago P, 2000.

Liddell, Henry George; Scott, Robert; et al. A Greek-English Lexicon. 9th ed. with revised supplement. Oxford: Clarendon, 1996.

Wilke, Christian Gottlob. A Greek-English Lexicon of the New Testament: Being Grimm Wilke’s Clavis Novi Testamenti. Trans. Thayer, Joseph Henry. Ed. Grimm, Carl Ludwig Wilibald. Rev. ed. New York: American Book, 1889.

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