Abstract. This is the second of four papers that study algebraic and analytic structures associated with the Lerch zeta function. The Lerch zeta function ( s , a , c ) : = n = 0 e 2 i n a ( n + c ) s $ \zeta (s,a,c) := \sum _{n=0}^\infty \frac{e^{2 \pi in a}}{ (n+c)^{s}} $ was introduced by Lipschitz in 1857, and is named after Lerch, who showed in 1887 that it satisfied a functional equation. Here we analytically continue ( s , a , c ) $\zeta (s, a, c)$ as a function of three complex variables. We show that it is well-defined as a multivalued function on the manifold : = ( s , a , c ) ( ) ( ) , ${\mathcal {M}}:= \lbrace (s, a, c) \in {\mathbb {C}}\times ( {\mathbb {C}}\setminus {\mathbb {Z}}) \times ( {\mathbb {C}}\setminus {\mathbb {Z}}) \rbrace ,$ and that this analytic continuation becomes single-valued on the maximal abelian cover of ${\mathcal {M}}$ . We compute the monodromy functions describing the multivalued nature of this function on ${\mathcal {M}}$ , and determine various of its properties.