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Three-dimensional exactly solvable model of electron movement in the periodic separable Lame potential

One-gap and two-gap separable Lame potentials are studied in detail. For onedimensional case we construct the dispersion relation graph E(k) and for threedimensional case we construct the Fermi surfaces in the first and second bands. The pictures illustrate a passage from the limit case of free electrons to the limit case of tight binding electrons. These results are used to describe the Lifshits electron phase transition of 2 2 kind and derive some exact expressions. We also examine singularities of the second derivative of magnetic momentum in an external magnetic field. The parameter of the singularities depends on corresponding effective mass.