I'm sure there are others, but an easy example would be the fracturing of the Mongol empire around Kublai Khan's reign.
Kublai was Ghengis' grandson, and there were civil wars and succession issues when he rose to power due to the previous Khagan (Möngke Khan, Kublai's elder brother) having no definitive heir when he died. By Kublai's death the Mongol empire had split into four functionally sovereign states, eventually ending the largest contiguous empire in history.
A little slower than Lucius' kids, but there's one of the largest empires breaking up in just a couple generations.