"She eats" is not technically the same as "she is eating" - the latter is progressive - therefore they are translated into Italian differently ("lei mangia" / "lei sta mangiando"). Both "She eats" and "She is eating" both have the same French translation as French simply does not have a progressive tense or an equivalent.
Lei is she referring to a person we are talking about, in third person. The other case is different. I try to explain: If you want to refer in a formal way to a person you dont know, or a elderly, or your boss, etc..to someone you dont have confidence *usually a stranger, u use "Lei"., in place of "You", even if you are speaking directly to him/her. U need to think about those things, to spot the difference (Formal/informal)
I'm pretty sure it's conjugated equally or in the same manner. You just discern through context; once you are in the situation you will recognize so I wouldn't worry about that; I'd just instead keep in mind the nuance. Again, it's been over a month since I've even looked at my Italian flashcards, but I think it's the same with other romance languages that use the third person interchangebly with the first person singular formal.