Skyrim Walkthrough: Lights Out Quest

You get the "Lights Out!" Sidequest in Solitude. Locate an Argonian character named Jaree-Ra. Find him near Bits and Pieces or Angeline's Aromatics. He will ask you if you are new here and will tell you he is new here too, and that you two could be friends and help each other. He will ask you if you want to make some easy gold. Ask him what he has in mind. He will tell you his sister Deeja and him are treasure hunters who like to collect things. Tell him you are listening. He will tell you many ships come through the docks that pass through dangerous waters. He is interested in a particular ship, the Icerunner. It is to be guided to the docks by the lighthouse, but if the fire on the lighthouse were to go out, it will be stuck and you can raid it. He wants you to put out the lighthouse fire. There will then be loot to be shared

Ask him what would happen to the sailors on the boat. He will tell you that he will make sure they wash up safe to shore, maybe even they'll pay you for their "rescue". He tells you it would be best if you two spoke little until you have completed your task.

Open your quest journal.

Lights Out!
Jaree-Ra has asked me to put out the Solitude lighthouse fire.

Objectives:
Put out the fire in the Solitude Lighthouse.

Exit Solitude and head down the road, passing Katla's Farm. Reach the river and travel Northeast past the East Empire Company Warehouse. Pass near a big ship, and then you reach the lighthouse. Climb up the spiral stairs all the way to the top of the lighthouse. If you are spotted by the lighthouse keeper Ma'zaka, kill him. Put out the fire. Now you need to return to Jaree-Ra and find out if a ship has crashed.

Fast travel to the East Empire Company Warehouse south of Solitude. Climb up the wooden stairs and speak to Jaree-Ra. Tell him you put out the lighthouse fire. He will tell you that the effects have already been felt, that the Icerunner has failed to dock on time and has run aground on the eastern coast. His sister Deeja will be at the wreck with their Blackblood Marauders. You are to head up to Solitude's eastern shoreline to find where it's run aground and meet Deeja. Your objective now is to find Deeja at the Wreck of the Icerunner.

Head to the NE, and swim across the river to the Icerunner wreck. Enter the Ice runner and find Deeja. She will tell you her brother told her you were coming, and to give you what you earned. Talk to her and ask her if you are splitting the loot. She will tell you the loot has already been moved and that you have earned a quick death!

Kill Deeja and the other Blackblood Marauders on the ship. Look at the quest log:

"Jaree-Ra has betrayed me and taken the loot from the Icerunner. I've defeated his sister Deeja, now I must track down Jaree-Ra"

Your objective is to find out where Jaree-Ra's bandits took the loot. 

Read the Note from Jaree-Ra you looted from Deeja's corpse. It says:
"Sister, Once you have picked up the packages send them on to me at the Broken Oar Grotto. The fool who did our work at the lighthouse should arrive shortly. Thereafter, make sure he is taken care of"

Fast Travel to the Solitude lighthouse and from there head Northwest to the Broken Oar Grotto. Enter the Grotto. Your objective now is to defeat Jaree-Ra. Climb upstairs to the platform killing Black Blood Maruaders along the way. Hear NE and then North. When you get near the ship, use the lever to lower the drawbridge and cross it into the ship. There will be lots of blackblood marauders there. They aren't hard to defeat individually, but since there are many of them, take care not to get ganged on. Defeat them, and kill Jaree-Ra to complete the quest. Then search the ship for any  gold and  treasures (including a Cherim's Heart skillbook that will increase your Smithing skill) and leave the Grotto.