A set $S\subset \R^d$ is $C$-Lipschitz in the$x_i$-coordinate, where $C>0$ is a real number, if, for every two points $a,b\in S$, we have $|a_i-b_i|\leq C \max\{|a_j-b_j|\sep j=1,2,\ldots,d,\,j\neq i\}$. Motivated by a problem of Laczkovich, the author asked whether every $n$-point set in $\Rd$ contains a subset of size at least $cn^{1-1/d}$ that is $C$-Lipschitz in one of the coordinates, for suitable constants $C$ and $c>0$ (depending on $d$). This was answered negatively by Alberti, Csörnyei and Preiss. Here it is observed that a combinatorial result of Ruzsa and Szemerédi implies the existence of a 2-Lipschitz subset of size $n^{1/2}\varphi(n)$ in every $n$-point set in $\R^3$, where $\varphi(n)\to\infty$ as $n\to\infty$.