Nevertheless for David's sake did the LORD his God give him a {b} lamp in Jerusalem, to set up his son after him, and to establish Jerusalem:

(b) Meaning, a son to reign over Judah.

Wesley's Notes

15:4 A lamp - A son and successor to perpetuate his name and memory, which otherwise had gone into obscurity. Jerusalem - That he might maintain that city, and temple, and worship, as a witness for God, in the world, against the Israelites and heathen world.

King James Translators' Notes

lamp: or, candle

Jamieson-Fausset-Brown Bible Commentary

4. for David's sake did the Lord his God give him a lamp-"A lamp" in one's house is an Oriental phrase for continuance of family name and prosperity. Abijam was not rejected only in consequence of the divine promise to David (see on [314]1Ki 11:13-36).

Matthew Henry's Concise Commentary

15:1-8 Abijam's heart was not perfect with the Lord his God; he wanted sincerity; he began well, but he fell off, and walked in all the sins of his father, following his bad example, though he had seen the bad consequences of it. David's family was continued as a lamp in Jerusalem, to maintain the true worship of God there, when the light of Divine truth was extinguished in all other places. The Lord has still taken care of his cause, while those who ought to have been serviceable thereto have lived and perished in their sins. The Son of David will still continue a light to his church, to establish it in truth and righteousness to the end of time. There are two kinds of fulfilling the law, one legal, the other by the gospel. Legal is, when men do all things required in the law, and that by themselves. None ever thus fulfilled the law but Christ, and Adam before his fall. The gospel manner of fulfilling the law is, to believe in Christ who fulfilled the law for us, and to endeavour in the whole man to obey God in all his precepts. And this is accepted of God, as to all those that are in Christ. Thus David and others are said to fulfil the law.