Consider a conventional subsonic airfoil in level flight. Typically it is cambered and with a small positive incidence, both of which features contribute to lift.
Now droop the leading edge, as with say a plain leading-edge flap. This reduces the incidence, possibly even taking it negative, but increases the camber. Will the net lift increase or decrease, and why? Can the answer vary according to other flight conditions?
From this NASA study on LE flap/droop for a light general aviation wing:
Variations of lift are small up to $\alpha$ 10°, but the stall is delayed to a higher angle of attack (and $C_L$) for a full-span droop (see: How do droops help to avoid stalls?).
And from a NACA study published in 1954 (NACA-RM-SA54B16) on the Effect of a Leading-edge Flap upon the Lift, Drag, and Pitching Moment of an Airplane Employing a Thin, Unswept Wing:
The variations of lift with angle of attack and of pitching moment with lift near zero lift were not significantly affected.
In general at all test Mach numbers, the drag at zero lift increased with flap deflection.
The maximum lift-drag ratio was increased at subsonic speeds, and the increment in the maximum lift-drag ratio for a given flap deflection decreased as the Mach number approached unity. At supersonic speeds, flap deflection had no influence upon the maximum lift-drag ratio.
(Above plot shows the round leading edge data at Mach 0.6; left-to-right: $C_D$, $C_L$, and $C_m$.)
Note: The second study is on a thin airfoil, but the core premise (reduction of incidence and increase of camber) is covered here.
