Albert Barnes Commentary 1 Samuel 20:3

"And David sware moreover, and said, Thy father knoweth well that I have found favor in thine eyes; and he saith, Let not Jonathan know this, lest he be grieved: but truly as Jehovah liveth, and as thy soul liveth, there is but a step between me and death." — 1 Samuel 20:3 (ASV)

And David swore moreover — Rather, “yet again.” He met Jonathan’s denial by repeating his statement and confirming it with an oath.