Learn Italian: Passo da Luca presto. - I am dropping by Luca's early.

This is a special rule in Italian! When you are going to or stopping by a person's house, room, or business, you use the preposition da. Think of da Luca as meaning "to Luca's place."

Does passo literally mean "I drop by"?

Passo is the "I" form of the verb passare, which literally means "to pass." When you talk about passing by a person's house or shop, it translates perfectly to "dropping by" or "stopping by" in English.

Can presto also mean "soon" instead of "early"?

Yes! Presto means both "early" and "soon." Depending on the context, this sentence could just as easily mean "I am dropping by Luca's soon."

Why is the word for "I" missing from this sentence?

In Italian, the verb ending tells you who is doing the action. The -o ending in passo already tells us it is "I" doing it. You leave the io out unless you really want to emphasize that you are the one dropping by.