Given a unimodular group, the Wiener-Tauberian theorem said:
"Every two sided (or one sided) ideal in $L^1(G)$ is contained in a two sided (or one sided) maximal ideal."
But based on the Krull's theorem (that asserts that a nonzero ring has at least one maximal ideal, hold also for noncommutative rings) this result is always true.
Note that Krull's theorem works for unital rings only and $L_1(G)$ is unital if and only if $G$ is discrete. Indeed, there are non-unital rings (even Banach algebras) without maximal ideals at all. (One such example is the Volterra algebra). In this respect, the theorem says that $L_1(G)$ behaves nicely, even without the presence of the unit.