Suppose that $L_1$ is a regular language and $L_2$ is a context-free language. Which one of the following languages is NOT necessarily context-free?

Let $L_1$ be a regular language and $L_2$ be a context-free language (CFL).

1. Intersection ($L_1 \cap L_2$): Context-free languages are closed under intersection with regular languages. The cross-product construction of a Pushdown Automaton (PDA) and a Deterministic Finite Automaton (DFA) yields a PDA. Thus, $L_1 \cap L_2$ is always context-free.

2. Concatenation ($L_1 \cdot L_2$): Since regular languages are also CFLs, this is the concatenation of two CFLs, which is always context-free.

3. Union ($L_1 \cup L_2$): CFLs are closed under union. Since $L_1$ is regular (and hence context-free) and $L_2$ is context-free, $L_1 \cup L_2$ is always context-free.

4. Difference ($L_1 - L_2$): By set theory, $L_1 - L_2 = L_1 \cap \overline{L_2}$. If $L_1 - L_2$ were always context-free, then choosing $L_1 = \Sigma^*$ (which is regular) would mean $\Sigma^* - L_2 = \overline{L_2}$ is always context-free. However, CFLs are not closed under complementation. Therefore, $L_1 - L_2$ is not necessarily context-free.

Hence, the correct option is (C).