  In [Solving second order ordinary differential equations by extending the
Prelle-Singer method, J. Phys. A: Math.Gen., 34, 3015-3024 (2001)] we defined a
function (we called S) associated to a rational second order ordinary
differential equation (rational 2ODE) that is linked to the search of an
integrating factor. In this work we investigate the relation between these
$S$-functions and the Lie symmetries of a rational 2ODE. Based on this relation
we can construct a semi-algorithmic method to find the Lie symmetries of a 2ODE
even in the case where it presents no Lie point symmetries.
