Albert Barnes Commentary 1 Kings 2:4

"That Jehovah may establish his word which he spake concerning me, saying, If thy children take heed to their way, to walk before me in truth with all their heart and with all their soul, there shall not fail thee (said he) a man on the throne of Israel." — 1 Kings 2:4 (ASV)

That the Lord may continue his word: The original promise given to David indirectly through Nathan (2 Samuel 7:11–17), though apparently unconditional, was later made conditional upon continued obedience. David reminds Solomon of this to impress upon him a powerful motive to remain faithful and obedient.