I_a is an arbitrary constant that determines how much ambient light there is (and what color it is)
As mentioned in lecture, $$k_a$$ is also a constant determined by the material itself. Does it mean that $$L_a$$ could be regarded as a constant by human manipulation of parameters?
Certainly feels that way-- especially with how much they emphasize how "hacky" this is meant to be. I'm pretty sure Ambient Shading exists inside the Reflection Model in order to account for other negligible light sources in the background outside of the scene.
The ambient term is designed to be an approximation of multi-bounce lighting (you will learn this later in the course!). It's totally human controlled