Jamieson, Fausset and Brown on Hosea 1:9

9. Lo-Ammi--once "My people," but henceforth not so (Eze 16:8). The intervals between the marriage and the successive births of the three children, imply that three successive generations are intended. Jezreel, the first child, represents the dynasty of Jeroboam I and his successors, ending with Jehu's shedding the blood of Jeroboam's line in Jezreel; it was there that Jezebel was slain, in vengeance for Naboth's blood shed in the same Jezreel (1Ki 16:1; 2Ki 9:21, 30). The scenes of Jezreel were to be enacted over again on Jehu's degenerate race. At Jezreel Assyria routed Israel [Jerome]. The child's name associates past sins, intermediate punishments, and final overthrow. Lo-ruhamah ("not pitied"), the second child, is a daughter, representing the effeminate period which followed the overthrow of the first dynasty, when Israel was at once abject and impious. Lo-Ammi ("not my people"), the third child, a son, represents the vigorous dynasty (2Ki 14:25) of Jeroboam II; but, as prosperity did not bring with it revived piety, they were still not God's people.