Many uses for a lighthouse
You'd think so, but actually lighthouses are just general navigation beacons.
You get big powerful ones that you can spot from far away as you approach the coast from the sea, these tell you basically which part of the coast you're approaching. Then you might get a smaller lighthouse to signal the clear water channel to approach a port. Any dangers they warn about are basically irrelevant to a boat of less than a ton.
Also many lighthouses don't illuminate 360 degrees. If only because then the local villagers can't sleep, but also to only cover a particular danger or channel. So even if it was working its feasible that it wasn't identifiable in the fog.