 Solution

If ${\lambda }_0=0$, the action has the exact discrete symmetry $\varphi \mapsto -\varphi$. Integrating out modes and rescaling preserve this symmetry, so no odd operator such as ${\varphi }^3$ can be generated from the even quartic coupling. Thus $g_0$ corrects $\lambda$ at no order in perturbation theory: the hypersurface $\lambda =0$ is invariant under the renormalization-group flow.