For countable things: many = a lot of.
- I have a lot of books = I have many books (e.g. I have 5 books)
For uncountable things: much = a lot of.
- I have a lot of money = I have much money (you cannot have 5 money, so it is uncountable)
- I have a lot of water = I have much water (you cannot have 5 water)
Saying, "I have much money [water, etc.]," would certainly sound odd to this native English speaker. While formally correct, that construction in particular is almost never used, at least colloquially. You will often hear something like, "My boss drinks or a lot of [or too much] coffee," but not, "My boss drinks much coffee."
What about if they're talking about their manager to other people? I'm an Australian, and I'd call my manager my manager if I were referring to her in front of her (e.g. introducing her to other people), but if I were talking to other people who don't know her and she wasn't there, I'm more likely to call her my boss.