Is this also potentially an imperative? Dà ought to operate as the imperative "You give me" command, shouldn't it? So, could this mean "Give me food" as a command?
This is the conjugation of the verb "dare"
"dà" is present, third person, singular. You automatically know from this word that the subject is "lui/lei".
"mi" = "me" or "a me" ("a me" in this case), that are object and indirect object.
Subject LUI/LEI (yes, the subject is implied, we can imply the subject in Italian)
Object MI (if it would be subject, it should be IO, like I and ME in English)