Hi!
You have used natural=coastline for this island, but natural=coastline is not for islands in lakes, only for islands in the sea.

For this island in the lake, you should convert the lake into a multipolygon relation and then add the lake as "outer" member and the island as "inner" member. 
Here is an example of a similar lake with islands: https://www.openstreetmap.org/relation/5516281

Let me know, if you have no experience with that, then I can do it, and you can inspect it later to see how it is done.