You can, but you will need to use the "folder sharing" feature available only to premium and/or enterprise customers. You will have a "corporate" account that shares a folder with your separate "employee" accounts that can be given read-only access to the passwords you put into the shared folders and control from the "corporate" account. It is not a feature that comes with the "free" accounts, although I believe that the free accounts can be the employee accounts, they just can't share anything back or have their own shared folders. I don't have or need that kind of setup, but I think that's how it might work for you.
As others have said, if LastPass, at whatever point, has the password and is pushing it into your browser viewing a login page, the browser can see the password at that point. To do better than that, the website would have to use multi-factor authentication or one-time-password tokens, and that's not something you, as the user of the website, get to decide, unless it's your website.
While you can add multi-factor to LastPass, that's just for accessing LastPass, not for the websites whose passwords you store in LastPass. It does not magically add two-factor or multi-factor to the internet, unfortunately. Whoever figures out how to do that will be very, very wealthy.