https://www.youtube.com/watch?v=lc9dABOpu4Q is this a good execution? Can it hurt lumbaries? Is it correct to do demi-reps?
No, that's not good execution. During bench press, your feet should stay in contact with the floor, and your butt and shoulder blades should stay in contact with the bench and your motion should be smooth and controlled. In this case, his but is coming off the bench in order to "cheat" the reps. This makes your position less stable and increases the risk of injury to your back. You back should be arched with your butt and upper back remaining in contact with the bench at all times. It is important to utilize leg drive during bench press, but that does not mean lifting your butt off the bench.
I will assume you are also asking about "semi-reps" or more commonly called "partial reps". These can be useful, but the way they are done in that video is incorrect. Again he is cheating the reps by lifting his body off the bench to initiate the half rep.
Partial reps are useful for maintaining specific tension on the muscle (increasing time under tension). To correctly perform partial reps for bench you would keep you body steady and in contact with the bench (aka proper bench form). The range of motion would be just from just above the chest to about 3/4 from lockout. You can adjust this to what feels right; whatever feels like it keeps the tension in your chest. As always, these reps should be smooth and controlled.
These guys give a much better bench press tutorial: https://www.youtube.com/watch?v=gRVjAtPip0Y (BUFF Dudes)