Lexical Definition

‎καταλλάσσω‎ katallássō (kat-al-las'-so) to reconcile ^G:V
from ‎κατά‎ and ‎ἀλλάσσω‎

reconcile.

• to change mutually, i.e. (figuratively) to compound a difference

Abbott-Smith

κατ-αλλάσσω (Att. -ττω; cf. ἀλλάσσω), [in LXX: Je 31 (48):39 (חתת), II Mac 1:5 7:33 8:29*;]
prop., to change, exchange (esp. of money); hence, of persons, to change from emnity to friendship, to reconcile (for exx. in cl., v. Thayer, LS): of the reconciliation of man to God (Lft., Notes, 288; ICC on Ro 5:10; DCG, ii, 474, 797), II Co 5:18, 19; pass., Ro 5:10, II Co 5:20; of a woman returning to her husband, I Co 7:11 (cf. ἀπο-καταλλάσσω).†

Abbott-Smith References

Liddell-Scott-Jones

καταλλάσσω-άσσω,

Attic dialect καταλλάσσωάττω, change money, [Refs 1st c.AD+] (also in middle, [Refs 4th c.BC+]:—passive, Matreas cited in [Refs 2nd c.AD+], with a play on signification [Refs]; change or give away, τὴν Χάριν τῶν νόμων for the laws, [Refs 4th c.BC+]; καταλλάσσωάσσειν τὸν βίον to leave life, [Refs 2nd c.AD+]

__b absolutely, transgress, contravene regulations, [Refs]
__2 middle, exchange one thing for another, ἡδονὰς πρὸς ἡδονάς [Refs 5th c.BC+]; ἀντί τινος πάντα [Refs 4th c.BC+]: absolutely, exchange prisoners, [Refs 2nd c.AD+]
__II change a person from enmity to friendship, reconcile, σφέας [NT+5th c.BC+]middle, καταλλάσσωάσσεσθαι τὴν ἔχθρην τινί to make up one's enmity with any one, [Refs 5th c.BC+] —passive, especially in aorist κατηλλάχθην or κατηλλάγην (former preferred by Trag., latter in Prose), to become reconciled, τινι [Refs 5th c.BC+]; θεοῖσιν ὡς καταλλάσσωαχθῇ Χόλου that he may be reconciled to them after his anger, [Refs 5th c.BC+]
__II.2 passive, of an offence, to be atoned for, φόνον ἐπιγαμίαις μὴ καταλλάσσωάσσεσθαι μηδὲ Χρήμασιν [Refs 3rd c.BC+]

_{LSJ Scripture Refs: 2Cor.5.19}