The bonus objectives in the Lighthouse are weapons crates Fisher can identify using electromagnetic vision.

The empty jail cell past the cave with the diesel generator.
The tunnel right before Morgenthal's torture chamber, with a diesel generator.
Past Morgenthal's torture chamber, there are two tents outside; one of the tents has a box.
Below the wooden walkway leading to the laptop referred in Grim's transmission. This small outside area has two guards talking about Lacerda's whereabouts that leads to the cancellation of the Eliminate Lacerda objective.
The small room next to the cannons on the rampart.