Why is this language regular?
Short answer. The language $L_1$ is clearly regular. Further, $L_3 = L_1L_2^{-1}$ is a quotient of $L_1$ and hence it is regular since the quotient of a regular language by any language (regular or not) is regular. So you don't care about $L_2$, but you do care about $L_1$.

More details. Let $L$ and $R$ be languages. Then $LR^{-1} = \{ u \in A^* \mid ur \in L \text{ for some }r \in R\}$. Therefore $LR^{-1} = \bigcup_{r \in R} Lr^{-1}$. If $L$ is regular, there are only finitely many languages of the form $Lr^{-1}$, each of which is regular (this is the dual form of Nerode's lemma) and hence $LR^{-1}$ is a finite union of regular languages and thus it is regular.