Saddanīti's author derives it from the root pāl to protect, as well as pāli, "dike, margin, edge, row, line" and ali, "dike" and paṭipāṭī (< Skt. pari-pāṭi, "succession, order" = Pāli pāli, "line", related to Skt. pāra, "shore, end, limit").
The dike refers to a passage in AN
4, 27910-14 where the Buddha talks about building a dike around a lake so the water doesn't overflow, comparing it to Vinaya principles not to be transgressed. The "succession" refers to Pj 2, 8710, re: monks begging for alms in a row (piṇḍāya caramānā rājaṅgaṇe pāḷiyā agamaṃsu). Note Burmese variant paṭipāṭiyā for pāḷiyā.
Childers has many references to the word usage of pāli in the commentaries and chronicles where it is always used in the sense of a "line" of text, as opposed to the commentaries; that is, it means pariyattidhammo.
Mayrhofer also has a discussion of the word's derivation (1963, vol. 2, 263-264) and suggests that it might be the result of "aus mehreren Quellen zusammengeflossen" (flowing together of many sources). Among the possibilities he cites (from various studies) are pāli-bhāsā < paribhāṣā (Skt. "rule, maxim"), perhaps from Dravidian (Kannada pār̤i, "row, line" or Telegu pāḍi "justice,
propriety"), or from pra + vṛt or ā + vṛt, "return, revolve, repeat" from which āvali and āli ("row, range") are derived, according to one source.
The primary meaning of pāli seems to be "row" or "line" (and "dam" by extension) which all the above words share (except pal, "to protect", although that too may relate to a "line" of defence), referring to the "line" of Buddha's teaching, either envisaged as the successive words of an transmission, the lines in a single text, or the continuous thread uniting all his teachings. Pāli had the meaning of (a line in) the sacred texts by the time of the commentaries and – as Petra has said – apparently first took on the meaning of an actual language in the 13th century.
Best wishes,
Bryan