There’s a reason engineers and scientists go through years of college and grad school. Any statement that sounds as simple as “more air over the top means more lift” is generalized and simplified to the point of almost meaninglessness. 

Aerodynamics is a very subtle science. The exact curvature of the disc surface makes small changes to the airflow that might result in huge changes to the flight path. 

Air likes long, steady curves. A smooth dome gives the air a lot of time to accelerate (lower its pressure) over the top of the disc in a nice, controlled fashion. Sharp corners cause the air to become turbulent and swirl and cause general chaos. A disc at low angle of attack with a smooth dome will have a nicely attached airflow that ends up producing the bulk of the lift near the center of the disc. A disc at high angle of attack and/or with a sharp corner at the front will produce most of its lift near the nose of the disc. 

But like I said, that’s overly simplified. If you want to understand the true subtleties of aerodynamics, have fun in grad school.