Suppose that \(f\) is a locally Lipschitz function defined on a Hilbert space, which satisfies the growth condition \[ -{C\over 2}(\|x\|^2+ 1)\leq f(x)\leq {C\over 2}(\|x\|^2+ 1). \] It is proved that the Clarke subdifferential \(\partial f(x)\) (of \(f\) at \(x\)) can be represented by the derivatives of its Lasry-Lions regularizations \((f_\lambda)^\mu\) as \(\partial f(x)=\overline{\text{co }}A(x)\), where \(A(x)= \limsup\{((f_\lambda)^\mu)'(z)\); \(\lambda\to 0\), \(\mu/\lambda\to 0\), \(z\to x\}\) [see \textit{J.-M. Lasry} and \textit{P.-L. Lions}, Isr. J. Math. 55, 257-266 (1986; Zbl 0631.49018)]. For Lipschitz functions \(f: E\to\mathbb{R}\) defined on arbitrary Banach spaces, it is proved that \(\partial f(x)= w^*\)-closure (\(\text{conv }L(f,x)\)), where \(L(f,x)\) is a set also defined in terms of Lasry-Lions regularization functions. This fact completes a result due to \textit{J. Benoist} [C. R. Acad. Sci., Paris, Sér. I 315, 941-944 (1992; Zbl 0772.49009)], who was the first to notice the inclusion \(\subset\).