In GR, it is important to distinguish between coordinate acceleration and proper acceleration. The latter is what an object physically feels and measures. On the other hand, the former can be influenced by apparent acceleration such as spacetime curvature and choice of coordinates. Objects with no source of propulsion have zero proper acceleration and follow geodesics in spacetime; they are said to be in free fall.
In experiments 1 and 2, the lift is following a geodesic. Light beams also travel along geodesics. In the frame of the lift, the four-velocity of the lift is purely in the time direction (since it is stationary), while the four-velocity of light is at a 45-degree angle (note that we are measuring vectors at the same spacetime point, since the lift and light are at the same place at the same time). Therefore, locally, light travels in a straight line in both situations because geodesics are straight. As a result, they are indistinguishable. In fact, the equivalence principle states that from a free-falling perspective, spacetime always looks like flat Minkowski spacetime locally, so experiments must give the same results.
In experiment 3, the lift is no longer following a geodesic. It has a proper acceleration of $g$. In its frame, geodesics will appear to have (coordinate) acceleration and curve, just like how people standing on the surface of the earth (having an upward proper acceleration of $g$) sees free-falling objects accelerate relative to them.
To summarize, the accelerations of the lift in experiments 2 and 3 are very different types of acceleration. The lift in experiment 2 has coordinate acceleration but zero proper acceleration, but the lift in experiment 3 has proper acceleration.