Dishonored Guide: Rescuing Emily from the Lighthouse Undetected and Nonlethal in The Light at the End Mission
This mission is probably the easiest out of all of them, but regardless there are a few things that will make life much easier for a stealth approach. This guide explains how to rescue emily non-lethally and undetected.
There is a video with a visual guide at the end of this post.
First the best entrance to the lighthouse is through the sewers which are located to the far right of the right entrance:
At the top of the elevator all the guards are very easy to take out. After you get to the top area you can take out Hamerlock, but I chose not to. The best entrance to that area is over the roof, you will be able to drop down from above to eliminate Hamerlock. After you rescue emily the game is over.