In this work, we study the Lie-point symmetries of Kepler–Ermakov systems presented by C Athorne in J. Phys. A24 (1991), L1385–L1389. We determine the forms of arbitrary function H(x, y) in order to find the members of this class possessing the sl(2, ℝ) symmetry and a Lagrangian. We show that these systems are usual Ermakov systems with the frequency function depending on the dynamical variables.