Suppose $Y$ is a hypersurface of a smooth projective $X$. For which degree do we always get isomorphism for hard Lefschetz when we study the cohomology of $Y$?

Suppose $Y$ is a hypersurface of a smooth projective $X$. For which degree k values defined below, do we always get isomorphism when studying the cohomology of $Y$? What can be said about the general version of this? If $Y$ is a subvariety of codimension say $i$, to which codimension $i$ and to which $k$ do we get isomorphism between $H^{n - k}(X) \cong H^{n + k}(X)$?

If $Y \subset X$ is a subvariety that is possibly singular, where $X$ is a smooth projective variety, when is it true that the hard Lefschetz theorem holds, when we study the cohomology of $Y$?

Suppose $Y$ is a hypersurface of a smooth projective $X$. For which degree do we always get isomorphism for hard Lefschetz when we study the cohomology of $Y$?

If $Y \subset X$ is subvariety that is possibly singular, where $X$ is smooth projective variety, when is it true that the hard Lefschetz theorem holds, when we study the cohomology of $Y$.

If $Y \subset X$ is a subvariety that is possibly singular, where $X$ is a smooth projective variety, when is it true that the hard Lefschetz theorem holds, when we study the cohomology of $Y$?