It needs to be a closed mitre hip as suggested or an inverted hip. With the inverted you would have the left side acting like a valley and the right side hanging over like it is just now.
The lead also need to be a good bit wider than it currently is.
As above leads too narrow and badly fitted .
It could have had hip tiles bedded as per ridge .
I'd be inclined to remove the lead and put a hip tile on.
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