Ironically of course, David kills the Amalekite because he believes his lie (2 Sam 1:15-16). If the Amalekite had told the truth, he might have lived. In a further irony, David succeeds at something Saul had failed to do (i.e., kill Amalekites). At the same time, however, the Amalekite armor bearer lays claim to killing Saul — something that David, Saul's former armor bearer (1 Sam 16:21-22) would not or could not do. But perhaps the deepest irony is that Saul, although rejected by God from the kingship, remained "the Lord's anointed" and under divine protection to the last (2 Sam 1:14). Yet he could not protect himself from himself.
Stephen B. Chapman, 1 Samuel as Christian Scripture: A Theological Commentary (Grand Rapids: Eerdmans, 2016), 213.