Lift is by definition at right angles to the overall flow (not the orientation of the blade or wing, though they are often close to the same)
The direction of the flow can be relative to the turbine, or relative to the blade, in which case it would change direction from hub to tip, so there is probably a convention of taking it as relative to the turbine as a whole unless otherwise stated.
Drag is in the direction of the flow, at right angles to lift.
You can get a turbine to turn with drag alone, usually with the axis of rotation at right angles to the flow, almost always vertical, but they are generally less efficient.
Note: if you squeeze a pea (pip) it will take off much faster than you squeezed it.