  In this paper, we combine Lovelock gravity with gravity's rainbow to
construct Lovelock gravity's rainbow. Considering the Lovelock gravity's
rainbow coupled to linear and also nonlinear electromagnetic gauge fields, we
present two new classes of topological black hole solutions. We compute
conserved and thermodynamic quantities of these black holes (such as
temperature, entropy, electric potential, charge and mass) and show that these
quantities satisfy the first law of thermodynamics. In order to study the
thermal stability in canonical ensemble, we calculate the heat capacity and
determinant of the Hessian matrix and show in what regions there are thermally
stable phases for black holes. Also, we discuss the dependence of thermodynamic
behavior and thermal stability of black holes on rainbow functions. Finally, we
investigate the critical behavior of black holes in the extended phase space
and study their interesting properties.
