***Neither a teacher nor a native speaker.***
Hi and welcome
I believe "Let's get to know one another." has nothing to do with a direct object.
I want to get to know someone.
Let's get to know someone.
I want to watch some movies.
Let's watch some movies.
You can't say:
Let's know someone.
If you want to know who someone is, you have to get to know him/her.
Let's get to watch some movies.
At least this one sounds strange...
I hope I understood your question.