1 Kings 15:4 - Matthew Poole's English Annotations on the Holy Bible

A lamp, i.e. a son and successor to perpetuate his name and memory, which otherwise had gone into obscurity. The same phrase is used above, 1 Kings 11:36 2 Kings 8:19 2 Chronicles 21:7. To establish Jerusalem, i.e. that he might maintain that city, and temple, and worship, as a witness for God in the world against the Israelites and heathen world, who should have inquired after it, and embraced the true religion there established and set up, as a beacon upon a high hill, that all men might take notice of it.