Learn Italian: Oggi mangiamo da lui. - Today we are eating at his place.

While da often means "from", when you put it right before a person (like a name or a pronoun like lui), it means "at that person's house" or business. So, da lui means "at his place", just as da me would mean "at my place" or dal medico means "at the doctor's office".

What kind of pronoun is lui in this sentence?

It is a "tonic" or strong pronoun. In Italian, whenever a pronoun comes directly after a preposition (like da, con, or per), you must use this strong form. For "him" and "her", the tonic forms are lui and lei, which happen to look exactly the same as the subject words for "he" and "she".

Why is mangiamo translated as "we are eating" instead of "we eat"?

The regular Italian present tense covers both English forms. Mangiamo can mean either "we eat" or "we are eating" depending on the context. Because the sentence is about a specific plan for oggi (today), "we are eating" is just the most natural way to translate it into English here.

Where is the word for "we" in this sentence?