I noticed that the ticket for this museum was on the Natural History Museum of Los Angeles ticket website, does the fees cover for both this museum and the Natural History Museum, or do I have to buy separate tickets for this museum?

They are separate tickets. The two museums are a distance away from each other

Seperate single day tickets. Yearly membership covers both NHM and La Brea, plus a 3rd museum.

I also believe it is separate admission for this museum. Although, there may be a combo socal museum special you could look for.

I believe separate