ulaka muvappa eṉpatu lōkalōkaṅkaḷum eṇpattu nālu leṭcam āṟṟumākkaḷuñ canto[vi]ttaiy aṭaintu piḻaikkum paṭi. Which I tentatively translate as:

"The phrase ulaka muvappa (means) the manner in which (in) the worlds (lōkalōkaṅkaḷum) the eighty four lakhs of kinds (āṟṟu < āṟu, litteraly “way”) of people obtain salvation after obtaining knowledge (vittai = vidyā) of the poem (cantō < chandas, “sacred hymn; metre”)."

The mention of the 84 lakhs of living beings appears to be just a way to state, as the other commentaries do, that all living beings rejoice.

I have found references to this number of 84 lakhs in the Maitrāyaṇīya Upaniṣad (see van Buitenen, 1962, p. 102 and 129) as well as in the Rāmāyaṇa of Tulsidas, the Caitanyacaritāmṛta and in a 1499 CE inscription from Gujarat.

Could any one point out to me other sources (Pūrāṇas for instance) and, especially, sources where the this total of 84 lakhs is detailed?