Cannot be determined.
From the axiom $\lnot p \to q$, we can conclude that $p \vee q$.
So, either $p$ or $q$ must be TRUE.
$$\begin{align}
&\lnot p \lor (p \to q)\\[1em]
\equiv& \lnot p \lor ( \lnot p \lor q)\\[1em]
\equiv&\lnot p \lor q
\end{align}$$
Since nothing can be said about the Truth value of $p$, it implies that $\lnot p \lor q$ can also be True or False.
Hence, the value cannot be determined.