I'm not sure if I chose the right Version, but this is for the most recent version on Xbox One: Better Together (11/26/2017).
I synced one of my survival worlds from Xbox One Edition, and there are some areas that become super laggy (low FPS) when I walk into them.
The first area with huge lag is 3-4 hoppers connected together that are collecting eggs. The chest beneath was full, and the hoppers had full inventory of eggs. Once I removed the eggs from the hoppers, the lag seemed to have decreased significantly.
The next area with huge lag is in a barn containing horses. All of the horses were originated on my Xbox version. When I go into the horse barn, it is SUPER laggy, where I cant even turn my character or interact with any items. I also noticed the horses in there won't breed. I have suspicion that the synced horses might be causing this lag, or maybe the building they are housed in (there are no redstone devices or complicated machines in this area).
I also found this huge lag while exploring open terrain with no buildings. I was trying to fill in a map, and as I walked, random 15x15 block areas (estimated) start to lag similar to the other areas listed above. The lag in the open terrain isn't quite as bad as the hoppers and the horse barn.
Yesterday I was playing the world, and most areas were free of lag. However, the next day when I play my world again, new areas are beginning to lag. I am not sure what is causing this glitch, but it affects the game.
Most of this might be explained as the same problem as MCPE-28028, which describes lag that happens when mobs try to pathfind to a player but are stopped by a barrier of some kind. Since you were trying to breed the horses, you must have had food in your hand. In the open terrain, it might have been hostile mobs in shallow caves just below you trying to target you. I'm not sure about the eggs, but perhaps you had previously fed some seeds to some of the chickens laying them?
It's by no means certain that this is the same problem, but the pathfinding problem affects a lot of mobs in what seem like many different environments, and it's easy to misinterpret what triggers lag of any kind. So I'm just suggesting that you review MCPE-28028 (and perhaps the related ticket MCPE-28022) to see whether the conditions identified so far could explain your experiences with lag as well.