John Gill 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, and said
To assure Jonathan of the truth of it, that he did most certainly seek after his life, of which, as he had no doubt himself, by an oath he endeavoured to remove any that might be in Jonathan, who was not willing to believe his father could be guilty of so foul a crime:

your father certainly knows that I have found grace in your eyes :
that he was high in his favour, that he had a great value for him, and he had a large share in his love and friendship, and that was the reason why he hid from him his base intentions:

and he says, let not Jonathan know this, lest he be grieved ;
as he would be, both for the evil his father would be guilty of, and the danger David, his beloved friend, would be in:

but truly, [as] the Lord lives, and [as] your soul lives, [there is]
but a step between me and death ;
as appeared by his casting a javelin at him, (1 Samuel 18:11) , sending messengers to his own house to slay him, (1 Samuel 19:11) , and others to Naioth to seize him, (1 Samuel 19:20) , and coming himself thither with an intention to kill him, (1 Samuel 19:22 1 Samuel 19:23) .

And in each of these instances he had a narrow escape for his life; and this he declared in the most solemn manner by an oath, for the confirmation of the truth of it to Jonathan.