I’ve just finished reading Martyn Lloyd-Jones on 2 Peter\1/, and most helpful it was. He mentions the paradoxial nature of the phrase “the day of eternity” in 3:18 (p. 256), and although he makes a passing reference to one day being as a thousand years, he doesn’t comment any further about it. I wondered if Peter uses “day” because it will be a period then the sun rises never to set. It is not the time period that is in view, a mere 24 hours, but the character of the day: it is a period of light that will never diminish, since it is the light of the one to whom all the glory is due.
1. D. Martyn Lloyd-Jones, Expository Sermons on 2 Peter, Edinburgh: Banner of Truth, 1983.