Is there a relation between material choice and produced lift at rotation?
Yes.

Some materials are easier to shape (think composites versus metal) or stay in shape better over time or under stress (think metal versus wood). This difference between the intended and the actual shape will have the biggest material-related impact on lift.

If you slightly change the question and ask for useful lift (lift minus weight of the structure), the stiffness and relative strength of the specific material must be added to the comparison. Useful parameters are the ultimate strength relative to density (breaking length) or stiffness relative to density (strain length). A stiff structure deforms less under load, so its shape will change less. Ideally, the structure is shaped such that only under load it assumes the aerodynamically most advantageous shape while its elasticity helps it to avoid being overloaded (aeroelastic tailoring).

The surface finish is also material-related, but is more affected by the manufacturing method. A rough surface is better at very low flow speeds while a smooth surface is better at moderate to high flow speeds.