The lexica agree on the referent and disagree on the etymology. BDB, s.v. לֵוִי, calls the root and meaning dubious, lists the competing theories, and records explicit opposition to all of them from Kautzsch, Wellhausen and Stade. HALOT keeps לוה I (to join, accompany) apart from לוה II (to lend, borrow, give as a pledge), which is what allows the two main Hebrew derivations to be stated as alternatives. D. Kellermann's article on לוה and לֵוִי in Theologisches Wörterbuch zum Alten Testament IV (English: TDOT VII), whose etymological discussion runs to roughly pp. 501-506, concludes that Genesis 29:34 is wordplay rather than derivation, surveys the options, and even entertains the possibility that a tribe Levi and a functional class of Levites were originally distinct entities merged by homonymy. Roland de Vaux (Ancient Israel, English translation 1961, 358-359) lists three possibilities, a cultic whirling or dancing, a pledging or dedicating, and an attaching or accompanying, and himself prefers an original theophoric personal name, comparing the Amorite name lawi-ilu from Mari cited in Herbert Huffmon's Amorite Personal Names in the Mari Texts (1965, 225); Mary Buck's work on Amorite Ugarit has since questioned linking those Amorite elements to the Hebrew root. The best known comparative proposal, Fritz Hommel's derivation from an Old South Arabian (Minaean) term for a temple dedicant or priest, built on the South Arabian epigraphy of D. H. Müller and J. H. Mordtmann and later taken up by Sayce and Grimme, is recorded by BDB but is now largely set aside on two grounds: the inscriptions are late and imprecisely dated, so priority cannot be shown, and the direction of borrowing is indeterminate. Wellhausen, Stade and G. B. Gray took the name instead as a gentilic formed from Leah. A separate thread connects the root to twisting or coiling, the standard derivation of לִוְיָתָן (Leviathan), and is only speculatively relevant here. It is also widely noted that several early Levite names, above all Moses, are Egyptian in form.
On the institution, the master question is whether Levite was first a kinship term or first a vocation. The reference-work tendency, represented by Baruch Levine, treats it as a professional class recruited from several clans with the eponymous ancestor a late back-formation, and reads the hired, landless Levite of Judges 17-18 as the key evidence. Aelred Cody (A History of Old Testament Priesthood, 1969, 29-38) and de Vaux argue instead for an originally secular tribe that later took up the vocation, and many mediate by positing a secular tribe scattered as Genesis 49 remembers and reconstituted around sanctuary service. Alexander Rofé has argued for an originally Transjordanian tribe centred on the Nebo sanctuary, driven west by territorial loss and the Moabite destruction of that shrine; Cody and Menahem Haran proposed that Levites were the priestly class of the northern kingdom, absorbed at a lower rank in the south after 722.
On the hierarchy of priests and Levites, Julius Wellhausen's Prolegomena (English 1885, 121-157) made Ezekiel 44 the hinge: Josiah's centralization displaced the country Levites, Ezekiel justified their demotion, and the Priestly material systematized and retrojected it. Yehezkel Kaufmann and Moshe Greenberg (JAOS 70, 1950, 41-47) argued for the antiquity of the priestly institutions; Haran (Temples and Temple-Service in Ancient Israel, 1978) and Jacob Milgrom argued that the Priestly distinction is pre-exilic and independent of Ezekiel; Gunneweg (Leviten und Priester, 1965) had already placed it before Ezekiel; and Nathan MacDonald (Priestly Rule, BZAW 476, 2015) reverses the direction of dependence, reading Ezekiel 44 as a late polemical text dependent on Numbers 18. Milgrom's Studies in Levitical Terminology (1970) analyses the guard vocabulary and the encroachment taboo and reads the Levites as a buffer absorbing divine wrath on Israel's behalf; Levine's work on the given ones connects the Priestly description of Levites as a gift handed over to Aaron with Mesopotamian temple oblates. Frank Moore Cross (Canaanite Myth and Hebrew Epic, 1973, 195-215) reconstructed a long rivalry between a Moses-descended priesthood at Shiloh, Nob and Dan and an Aaronide priesthood at Bethel and Jerusalem, a reading extended by Richard Elliott Friedman and acknowledged to rest on late and tendentious genealogies. For the post-exilic expansion of Levitical roles see Sara Japhet and Gary Knoppers, especially Knoppers in JBL 118 (1999), 49-72, with the striking datum that Ezra 2:40 counts only 74 Levites against 4,289 priests. On Malachi's covenant with Levi see Julia O'Brien, Beth Glazier-McDonald and Andrew Hill; on the Second Temple elevation of Levi see James Kugel in HTR 86 (1993), 1-64, Robert Kugler, and the Greenfield, Stone and Eshel edition of the Aramaic Levi Document. Mark Leuchter (The Levites and the Boundaries of Israelite Identity, 2017) is the most recent synthesis. Levine stresses that no contemporary external documentation of the early Levites survives, so every one of these reconstructions rests on internal biblical evidence read against comparative material.