  We consider the general Lienard-type equation $\ddot{u} = \sum_{k=0}^n f_k
\dot{u}^k$ for $n\geq 4$. This equation naturally admits the Lie symmetry
$\frac{\partial}{\partial t}$. We completely characterize when this equation
admits another Lie symmetry, and give an easily verifiable condition for this
on the functions $f_0, \dots , f_n$. Moreover, we give an equivalent
characterization of this condition. Similar results have already been obtained
previously in the cases $n=1$ or $n=2$. That is, this paper handles all
remaining cases except for $n=3$.
