Is the restriction of a periodic function of several variables to a hyperplane also periodic?

Question

Consider a lattice $\Lambda \in \mathbb{R}^n$ and a function $f:\mathbb{R}^n \rightarrow \mathbb{R}$ s.t. $\forall x \in \mathbb{R}^n$, $l \in \Lambda$, $f (x + l) = f(x)$. Let $P$ be a hyperplane in $\mathbb{R}^n$. What can we say about the periodicity of the restriction $f|_P$?