It seems strange that a Philistine like Achish would swear by the LORD. In doing so he makes use of a well known oath formula (cf. 1 Samuel 14:39).1 Most likely he does so as a matter of courtesy and respect. In a polytheistic culture, people believed in the existence of many gods and were happy to acknowledge other gods
as and when it suited them.2 It is possible however that he developed an interest in the LORD based on what he saw of David and the success that he enjoyed.3
6 Then Achish called David and said to him, “As the LORD lives, you have been honest, and to me it seems right that you should march out and in with me in the campaign. For I have found nothing wrong in you from the day of your coming to me to this day. Nevertheless, the lords do not approve of you.