  We obtain families of non-isotopic closed exact Lagrangian submanifolds in
quasi-projective holomorphic symplectic manifolds that admit contracting
$\mathbb{C}^*$-actions. We show that the Floer cohomologies of these
Lagrangians are topological in nature, recovering the ordinary cohomologies of
their intersection. Moreover, by using these Lagrangians and a version of
Carrell-Goresky's integral decomposition theorem, we obtain degree-wise lower
bounds on the symplectic cohomology of these spaces.
