On the other side of the main port of Lopud, there is the bay of Šunj.
It is a proper beach, with incredibly hot sand and a restaurant/bar, and for that reason usually very crowded.
There are 2 main ways to get there: either for few kunas getting a taxi, some sort of vehicle which resemble a big golf cart,  or simply walking. As I wanted to visit the island first and then get to the island, I decided to walk.
The only suggestion I would give if you are going in the afternoon: bring water!