  We discuss the relationship between the Noether point symmetries of the
geodesic Lagrangian, in a (pseudo)Riemannian manifold, with the elements of the
Homothetic algebra of the space. We observe that the classification problem of
the Noether symmetries for the geodesic Lagrangian is equivalent with the
classification of the Homothetic algebra of the space, which in the case of a
Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime is a well-known result in
the literature.
