This paper is an investigation of $L$-dual frames with respect
to a function-valued inner product, the so called $L$-bracket
product on $L^{2}(G)$, where G is a locally compact abelian group
with a uniform lattice $L$. We show that several well known theorems
for dual frames and dual Riesz bases in a Hilbert space
remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.
