Makes sense - the backscatter is due to resonant Bragg scattering, so you'll pick up water waves of twice the wavelength of the radar (assuming you are looking pretty much downwards - there's a sin (alpha) term too, where alpha is the angle of incidence).
Means C-band will pick up 6 - 15 cm waves, which is probably a bit big for lakes. Should probably see them given a decent surface wind though? Or no? Most of the work I did was K-band, so I'm not sure.