In the following paper

" On actions of $SO(3)$ on lens spaces II" by S. Kim and J. Pak the following result (Lemma 1.1) has been used

Any effective action of $SO(3)$ on $L_{2n+1}(m)$, $m$ odd can be lifted equivariantly to an effective action of $SO(3)$ on $S^{2n+1}$. (Here $S^{2n+1}$ is sphere of dimension $2n+1$ and $L_{2n+1}(m)$ denotes Lens space.)

My query is if this result is true for free action? Can a free action of SO(3) on $L_{2n+1}(m)$, $m$ odd can be lifted equivariantly to a free action of $SO(3)$ on $S^{2n+1}$.