let=让,us=我们
let's 让我们。。。吧
Let's go see a movie.让我们去看电影吧
Let's eat.让我们吃吧/开动吧
Let's take better care of our environment.让我们更好的保护我们的环境
but usually ,in spoken chinese,when we say something like"let's blahblahblah" ,we just drop “让我们”
Let's go see a movie.去看电影吧
Let's eat.吃吧/开动吧
you can't dump让我们in the 3rd sentence you gave,b/c it's a formal way to say it.