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In the present note we give a construction (based on a retractional argument)of a Schauder basis for the Lipschitz free space $\mathcal{F}(N)$, over a net$N$ in any separable infinite dimensional $\mathcal{L}_\infty$-space $X$. Inparticular, this yields the first example of an infinite dimensional Banachspace $X$ not containing $c_0$ with such a property.

Schauder basis in Lipschitz free spaces over nets of $\mathcal{L}_\infty$-spaces