How do I walk to the lighthouse at the end of Paradise Island?
Quick Answer: You don't
Marking the western end of Paradise Island, the 'Hog Island Lighthouse' named after what Paradise Island used to be called sits at the edge of Paradise Island. There's no real way to walk there though from Atlantis, so don't really try. There's no road leading out there and in between the lighthouse and Atlantis are only private residences that you won't be permitted to walk through, unless you own them.
If you look at a map or even a satellite view of Paradise Island, it will look like you can get there and I suppose in a way you can, but you're probably better off not trying.
Like in the United States beaches in the Bahamas are public and the beach adjacent to Atlantis is no exception and you can walk this pretty far down Paradise, but then basically you hit an impressive enough barrier of rocks. In theory, one can climb over this, but one wrong step and you're at the edge of nowhere and nobody will be coming anytime soon. Furthermore, the rocks themselves sit close to the ocean and the surf hits onto them and you don't want to get caught in the tide and swimming around it really doesn't appear to be a good option either.
Thus the access to Colonial Beach, clearly listed on the maps, is geographically restricted. Reading between the lines, it would appear the people living on homes on the other side of the rock barrier, have created, effectively, a private beach for themselves.
Closest you'll get is a tourist boat taking people out to snorkel which naturally have to travel around Paradise Island. I posted the nicest picture first when the sun was clearer. All of these pictures are actually on the same day with the snorkel boat circling around the end of Paradise Island, the weather actually cleared up quickly, grey skies revealing blue skies quickly.