The major lexica divide the word along the same lines. LSJ lists three senses: physical or medical uncleanness (of wounds, vessels, and discharges), moral depravity (attested classically only by Demosthenes), and ceremonial impurity (attested only from the Septuagint). BDAG collapses these into a concrete sense ("refuse," at Matthew 23:27) and a moral sense of corruption, typically sexual, in Paul's vice lists. Louw-Nida likewise splits the word between the domain of clean and dirty objects and the domain of moral qualities. Hauck's TDNT article on the καθαρός word-group traces the movement from concrete filth, through Greek cultic and philosophical use, into the Septuagint's ritual system, and finally into Paul's moral usage, which never loses the connotation of what excludes from God's presence. Spicq and Moulton-Milligan add the documentary evidence that ἀκαθαρσία was the standard term in Egyptian house-lease contracts for the refuse a tenant had to remove.
In the Septuagint the word becomes the near-monopoly rendering of Hebrew טֻמְאָה, absorbing the whole Levitical purity system, and it takes on a strongly moral, idolatry-linked sexual coloring in Ezekiel and in Second Temple literature (Wisdom of Solomon, the Testaments of the Twelve Patriarchs, Psalms of Solomon). Jonathan Klawans' distinction between ritual impurity (bodily, temporary, not sinful) and moral impurity (from sexual sin, idolatry, and bloodshed, defiling both sinner and sanctuary) is now the standard framework, and on it Paul is not spiritualizing a merely ritual category but deploying an already biblical category of moral impurity. Scholars divide over whether Paul stands in essential continuity with this Second Temple stream (Klawans, Newton, Loader) or forges something genuinely new (Harper). The most-debated single verse is 1 Thessalonians 2:3, where Malherbe's influential reading of the impurity as corrupt motive is widely followed, against Balz's sexual reading.