After a little belt sanding, this is what I came up with. Those two screws are going to do double-duty: hold the lighthouse together and keep the LED in place too. And as you can see the clamps don't get in the way of the light either. Now it's time to make an adapter plate for the roof.
 

I've been thinking about how I was going to attach a roof to this lighthouse. What I came up with is to make an adapter plate first, and then the roof will attach to this plate. The material thickness below is 3/16" and will be round as you can see by my layout lines. I rough cut this out on my bandsaw first and now it's time to work on the lathe again.
 

A few minutes later I now have most of my adapter plate finished. This piece will go over the top of the lantern room, which will fit that piece exactly. The hole is going to be for a threaded fastener.
 

I'm using four # 6 screws to fasten it to the lantern room. And I'll make sure to have all the screw holes in the lantern room go between the windows where there is more material. Time to make a roof. 
 

First I machined the front so it fits over the adapter plate. Now I'm working at roughing out the roof-top. This is a slow process because I would remove some material, then cut the angle a small amount, then go back to roughing again and repeat.
 

Here are the three cutting tools that I've been using. The one in the middle is a parting tool or cutoff tool. I used this one a bunch. The one on the right I was using to cut the 30 degree angle with. And the other was used for roughing out material.
 

Once I got to this point, I had to decide if I wanted to reduce that diameter even more before cutting it off and possibly risking it getting away from me causing damage to it, or cutting it off and playing it safe. As you can see, I played it safe and I'll turn it around and machine away the extra.