Yes, they are stored in your PC for convenience (so you can still access them when offline). But why do you think you can log in from anywhere with your email and password to see your data? Because it is custodial

Just because they offer a cached offline access doesn't mean that they don't store your data. lol

Maybe check this?
https://support.logmeininc.com/lastpass/help/how-is-lastpass-safe-lp010089