What does it mean for a wing's lift distribution to be elliptical when the planform is not? How would you go about finding an equation for the lift coefficient of this wing where the lift distribution is known to be elliptical but the planform is not?
The (local) lift depends on many factors - not only the chord but also the profile, angle of incidence - and even up to the actual local flow. Without knowing the details of the actual wing, the distribution of lift can be hard to calculate.