Proving a language is not a regular language but a context free language
While it is possible to show that $L_2$ is not regular using the pumping lemma, it is easier to do so by making use of the fact that the regular languages are close under complement, i.e. a language is regular if and only if its complement is regular.

In order to show that $L_2$ is context-free, you can give either an automaton or a context-free grammar for the language. The automaton is presumably the easier way in this case. Hint: $L_2$ is a deterministic context-free language, so there is a deterministic PDA for $L_2$ that can be derived in a straightforward way from the deterministic PDA of $L_2$'s complement.