A space $X$ is said to be Rothberger if for each sequence $(\mathcal{U}_n)$ of open covers of $X$ there exists a sequence $(U_n)$ such that for each $n$ $U_n\in\mathcal{U}_n$ and $\{U_n : n\in\mathbb{N}\}$ is an open cover of $X$.

Give an example of a Rothberger space $X$ which has a Lindelöf subspace $Y$ that is not Rothberger.