I know it's several years late, but for anyone reading on... you can absolutely fly horizontal in a stall and you don't lose lift after you exceed critical AoA. obviously there is no aircraft designed such that you can produce the amount of thrust needed horizontally without a significant portion being vertical. Here is a Cl_alpha curve (Cl is just lift relative to the kinetic force of the wind or dynamic pressure) that kinda shows what happens after stall.
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After the peak and break, you see that lift does some wacky things. it drops a pretty significant amount and then kinda sticks around 75%, but it does not fall to zero. However drag obviously skyrockets, especially pressure drag. Another important thing to keep in mind is that lift is always perpendicular to V_inf (aka relative wind) and drag is always parallel. That is part of the definition of lift and drag.
Also, for something to fly ballistic means for there to be no significant lift to alter the course of the object. that means only drag and gravity. ballistic and uncontrolled are two different things as most planes would have to be controlled into flying ballistically but something like a ballistic missile is inherently designed to fly ballistically by putting the aerodynamic center significantly farther aft of the c.g..
