From Ancient Greek σέλινον.
The only Italian etymology I can find is on Wiktionary. And why does the Italian noun "sedano" look the same with the Italian verb "sedano"?
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"L'etimologico" by Alberto Nocentini says: "sedano" from "serano" from "seleno" from Byzantine Greek "sélinon" (σέλινον). The intermediate forms ("serano", "seleno") are attested in the Italian dialects, so they are no theoretical reconstructions.
Thus it's not a direct L > D sound change but an indirect one, probably due to the migration of the word from one dialect to another.
Remark about the LEI: This is a really large dictionary project which just has started. They haven't reached the letter S yet.
Addition, 1 hour later: You asked:
And why does the Italian noun "sedano" look the same with the Italian verb "sedano"?
That is coincidence, and nobody cared about it. The noun "sedano" and the verb "sedano" don't disturb each other because the speakers cannot confuse them. So there was no need to change the borrowed noun.