Runaway fenced mobs (sheep, cows, chickens) due to massive lag

When the game is struck with massive lag, even adjacent chunks struggle to load. Mobs spawn before fences and they frequently have time to wander out of their fence before it spawns in. While fixing the lag is ideal, it seems that the fences and terrain should spawn before the mobs to keep them from running away. Even if this source of lag is fixed, sooner or later another source will be introduced.

See screenshot.

Related: game crashes and lag occur almost every time I open a world. I would much prefer a larger save file so that the adjacent chunks do not have to generate whenever the world is opened!