A non-inertial reference frame could be accelerating, going in uniform circular motion, or at a specific gravitational equipotential surface. An observer in a non-inertial reference frame would observe the speed of light in another reference frame to be changing.
The lorentz factor, lower case gamma, is used to transform quantities like length, mass an time in one reference frame relative to another, co-moving (constant velocity) reference frame.
It is not, however, used in general relativity for the simple reason that the derivation of the lorentz factor was restricted ONLY to inertial reference frames.
The analogy is distances in a 2d map (measured as horizontal distance) are different in 3d (measured as slope distance). On a map, everything is flat but in 3d reality, all features on the map have different elevations.
And to take the analogy further, two points on the earth define a straight line (you can connect these two points with a laser) but, when you plot all the points in between on a map, you would discover that it is an s-curve called a geodesic (if the line is sufficiently long). It curves because at each point on the line, the north direction is changing.
When an observer is at an inertial reference frame (at rest or moving at a constant velocity, v), the speed of light is observed to be constant regardless of the velocity of that rf.
When an observer is at a non-inertial ref frame (accelerating, in uniform circular motion, and in the presence of gravity) the speed of light is observed to be changing depending on the acceleration of that ref frame.
The motion of any physical object is defined in a reference frame using x,y,z,t. In newtonian mechanics x,y,z and t are uniform quantities in any arbitrarily chosen reference frame. One can use any arbitrary unit and their measures will still be the same -- 1 foot=0.3048 meters, 1 minute=60 seconds, etc. In special and general relativity, space and time are not uniform quantities in all reference frames -- a foot in one rf is shorter that 1 foot in another rf. Clocks run slower in one rf than in another.
It is invariant ONLY in vacuum and ONLY in inertial reference frames. You can easily google 'speed of light is invariant' it will come up with what I am saying here -- it is invariant in inertial rf and variant in non-inertial rf.
In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics.