It is known that for Newton's second law to be valid it is fundamentally necessary that the system under study be an inertial reference, which automatically creates a direct dependence of the second law with Newton's first law. But does Newton's third law depend on the inertial frame or is it valid for any inertial or non-inertial system?
Third law does not hold in non-inertial frame. Let there be non-inertial frame moving with constant acceleration $\mathbf a$ with respect to inertial frame.
In that non-inertial frame, every body will experience apparent force $-m \mathbf a$ where $m$ is mass of the body. This apparent force has no counterpart.