For my simple brain, I've always remembered the lift formula as being related to the kinetic energy formula.
Momentum = mv
Kinetic Energy = 1⁄2 mv^2
‘Momentum’ of air = ρv
Dynamic Pressure = 1⁄2 ρv^2
Lift = 1⁄2 ρv^2 .S .C_L
May not be mathematically correct, but it works for me!