How do you know this? I've looked all over the internet and can't find any proof that Lightdm is more "lightweight" (whatever this means) or faster.

LightDM always felt rather sluggish to me. gdm3 appears to be a lot more snappy.

A display manager is the component of your Operating system responsible for launching your display server and the login session. This is the reason it is sometimes called the login manager. The layout of the screen that you see while entering your username and password(the greeter), your login session and user authorization are some of the tasks that the display manager performs.

A display manager presents the user with a login screen. A session starts when a user successfully enters a valid combination of username and password.

They all have about the same functions. Just use lightdm, or gdm if you're using gnome. Lightdm has all the same functions as gdm (gnome display manager), but it doesn't require gnome libraries.