Hi, Meursault, I think that by putting “lucky” as the first definition of “happy”, Chambers is showing that “happy” was originally formed from “hap”, whose definition as “chance, fortune, accident” is basically the same as the definition of “luck”. I don’t think it’s a particularly common present-day meaning for “happy”, though it’s not marked as “obsolete”.
However, the setter Stick Insect may have been thinking of the quote from Virgil’s Georgics, which begins with the answer to 22d and continues “qui potuit rerum cognoscere causas”. Wikipedia notes that the first word in the Latin quote is usually translated “fortunate”, though Dryden translated it as “happy”. Chambers gives “lucky”, but not “happy”, as a definition under the word “fortunate”.
But this is all rather academic – the clue to 22d would have worked just as well if it had read: “Happy man keeping priest’s effects.” Given the classical allusion, I’d have been happy (in the sense of “expressing contentment”) if the clue had read: “Fortunate man keeping priest’s effects.” But “lucky man” is pushing it.
We may be lucky to get a straightforward Listener crossword from time to time, but if we are after a challenge, we might not be happy.