Charles Ellicott Commentary 1 Kings 15:4

"Nevertheless for David`s sake did Jehovah his God give him a lamp in Jerusalem, to set up his son after him, and to establish Jerusalem;" — 1 Kings 15:4 (ASV)

Give him a lamp in Jerusalem. —Here, there is a brief allusion to the victory recorded in Chronicles, which obviously was the turning point in the struggle, saving the lamp of the house of David from extinction, and establishing Jerusalem in security. For David’s sake is, of course, for the fulfillment of the promise to David (2 Samuel 7:12–16). By virtue of the continuity of human history, the Divine law always ordains that, regarding consequences, the good deeds as well as the sins of fathers are visited on their children.