Proving that a language is a CFL
The language  $L' = \Sigma^* y\Sigma^*$ is regular and, by the closure properties of regular languages, so is $\Sigma^* \setminus L'$. Then, by the closure properties of context-free languages, $L_2  = L_1 \cap (\Sigma^* \setminus L')$ is context-free (since it can be written as the intersection of a context free language with a regular language).