Final answer:
Glucagon is the hormone that stimulates the breakdown of liver glycogen into glucose and starts gluconeogenesis for glucose synthesis from non-carbohydrate sources.
Step-by-step explanation:
The hormone responsible for causing the breakdown of liver glycogen back into glucose, and the synthesis of glucose by the liver from non-carbohydrate precursors, is glucagon. Glucagon inhibits the synthesis of glycogen and stimulates the breakdown of stored glycogen back into glucose via glycogenolysis. Additionally, this hormone stimulates the process of gluconeogenesis, where the liver converts amino acids and glycerol from fatty acids into glucose, replenishing blood glucose levels.