"I thought lighthouses were built on rock"
Yes, but there is generally a walkway around the windows at the top, and there can be a vertical drop of the rock on which the LH is built, hence enough sea could be below to accept a person without them hitting any rocks.
A drop of over 70 feet is something akin to falling onto concrete if one was falling onto a flat calm (from when I was in training for Merchant Navy and we were taught how to pilot a lifeboat, and why you should not jump from the deck into the sea as you could break both legs, hence need to descend in lifeboat if at all possible or to reduce height of the drop and get away from the ship ASAP).
So a drop onto a downward movement of the sea might not be life/leg threatening so long as you were able to get away from the rocks afterwards (not impossible either, depending on currents).
While the black screen and gunshot might be deemed rubbish, it leaves every option open (in case someone doesn't want to renew their contract). After all, Lindsey was hinting at the stress of not knowing if Danny would get back in one piece was not something she could put up with, wasn't she?
(Sorry, don't have any recording, going on memory before someone with Sky+ or a Humax box replays it and tells me it was Danny who was saying it cannot go on like this...)