I'm looking for a reference (or proof here) of the generalized RL Lemma for LCAGs. One result is that if $G$ is a LCAG then $$\{ \hat{f} : f \in L^1(G)\} \subset C_0(\Gamma)$$
where $\Gamma$ is the set of characters on $G$ (a character is a group morphism from $G$ to $\mathbb{T}$).