By real curve, we mean a Riemann surface $X$ together with an anti-holomorphic involution $\sigma : X\rightarrow X$. Let $S$ be a finite subset of $X$. For each point $x\in S$, we associate a positive integer $m_x\geq 2$. Then by Riemann existence theorem, there exists a universal covering $\pi : Y\rightarrow X$ such that $S$ is the branch locus of $\pi$ and $m_x$ is ramification index of $\pi$ over $x\in S$.
Question:- Is it true that the involution $\sigma$ can be lift to $Y$ making it real curve?