  We construct the 1- and 2-point integrable maps (B\"acklund transformations)
for the symmetric Lagrange top. We show that the Lagrange top has the same
algebraic Poisson structure that belongs to the $sl(2)$ Gaudin magnet. The
2-point map leads to a real time-discretization of the continuous flow.
Therefore, it provides an integrable numerical scheme for integrating the
physical flow. We illustrate the construction by few pictures of the discrete
flow calculated in MATLAB.
