The Greek alphabet starts from “alpha” and ends with “omega“. As for the lesser-known “lambda“, it comes in the 11th place among all 24 letters.

The midpoint is the 12th/13th letters, to which “lambda” is placed closest, hence the idea of holding an “average” position in the grand scheme of things.

If you land at the 11th/12th/13th/14th spot out of 24 competitors, you will reasonably qualify as “average/lambda“, being close to neither the victor “alpha” nor the “omega” finishing last.

I’d say something like:

Une grande chance comme ça n’arrive qu’une seule fois dans la vie de quelqu’un lambda comme moi !

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Précisément, l’usage de lambda comme “moyen” provient de l’école polytechnique