Belphegor had a history with Lucifer, an unpleasant one to be exact. It was because, during the everlasting war against Lucifer's siblings, Belphegor didn't participate at all and only sent demons to aid Lucifer. The only reason was that he was too lazy and he wasn't a demon that fancied blood and death by his own hands.
During the war, one of Lucifer's siblings approached him and persuaded him to turn his back on Lucifer. Although Belphegor didn't participate in the war, his loyalty was only to his creator, Lucifer. Lucifer listened to their conversation and decided to forgive him for his unwavering loyalty.
Lucifer couldn't hate Belphegor for his laziness because the way he thinks and the way Lucifer thinks were so similar. Belphegor helped the other Demon Kings to conquer the worlds they invaded thanks to his strategy, and so Lucifer made him his most trustworthy companion.
