Let $M \subset \mathbb C^n$ be a $C^2$ real hypersurface, let $p \in M$, and let $U \subset \mathbb C^n$ be an open neighbourhood of $p$. Let $\rho,\widetilde\rho \in C^2(U;\mathbb R)$ be local defining functions for $M$ on $U$, so that $M \cap U=\{z\in U:\rho(z)=0\}=\{z\in U:\widetilde\rho(z)=0\}$ and $d\rho\ne 0$, $d\widetilde\rho\ne 0$ on $M\cap U$. Suppose there is a real-valued function $a\in C^2(U;\mathbb R)$ such that $\widetilde\rho=a\rho$ on $U$. Then, for every $Z,W\in T^{1,0}_pM$,

\begin{align*} \mathcal L_{\widetilde\rho,p}(Z,W)=a(p)\mathcal L_{\rho,p}(Z,W). \end{align*}