Lyft have a deal with Grab here in Southeast Asia. As I understand I can use Grab to book Lyfts in areas where Lyft operates and Grab doesn't (and vice versa).
Not (always) vice versa. In Ho Chi Minh, where Grab operates, I was not able to book using Lyft and had to install/setup Grab.
OK, but that is more of a convenience for American tourists who may not have a local phone number to sign up for Grab than an actual service. People that live outside the US are not going to have the Lyft app in the first place.