The light house is closed at 4 pm, but the parking lot is still open for the walk to the beach ?

The Lighthouse is currently open 10am to 4pm, but hours are not the same as the state park hours. Visit the Park's web site to see their hours; during the summer, the park is usually open dawn to dusk.

Ive went around 5pm and they allowed us to walk around the beach.

Yes. The beach is walkable even after the lighthouse closes.

The park closes at dusk

Yes.