  We prove that the two-step flag variety $\mathcal{F}\ell(1,n;n+1)$ carries a
non-displaceable and non-monotone Lagrangian Gelfand--Zeitlin fiber
diffeomorphic to $S^3 \times T^{2n-4}$ and a continuum family of
non-displaceable Lagrangian Gelfand--Zeitlin torus fibers when $n > 2$.
