We investigate the steady motion of a liquid in a lake, modeled as a thin domain. We assume the motion is governed by Navier-Stokes equations, while a Robin-type traction condition, and a friction condition is prescribed at the surface and at the bottom, respectively. We also take into account Coriolis forces. We derive an asymptotic model as the aspect ratio δ = depth/width of the domain goes to 0. When the Reynolds number is not too large, this is mathematically justified and the three-dimensional limit velocity is given in terms of wind, bathymetry, depth and of a two-dimensional potential. Numerical simulation is carried out and the influence of traction condition reading is experienced.