John Gill Commentary 1 Samuel 20:8

"Therefore deal kindly with thy servant; for thou hast brought thy servant into a covenant of Jehovah with thee: but if there be in me iniquity, slay me thyself; for why shouldest thou bring me to thy father?" — 1 Samuel 20:8 (ASV)

Therefore you shall deal kindly with your servant
By informing him how his father's mind stood affected to him, that he might conduct himself accordingly, either by appearing at court, or by providing for his safety by flight:

for you have brought your servant into a covenant of the Lord with
you;
a covenant of friendship between Jonathan and David, of which Jonathan was the first mover, and so is said to bring or persuade him into it; called the covenant of the Lord, because made in his name and fear, and before him as a witness of it; and this David pleads as an argument with Jonathan, to deal kindly and faithfully by him in the present case:

notwithstanding, if there be in me iniquity, slay me yourself:
or pass sentence upon him to be slain; which, if guilty, he might have power to do in his father's absence, and which David desires might be done, notwithstanding the covenant of friendship between them, should he appear to deserve it by any action of his, of which he was not conscious; this expresses the strong sense he had of his own integrity, and served to confirm Jonathan in his opinion of it;

for why should you bring me to your father?
deliver him up into his hands to be put to a cruel death by him, or give him the trouble of doing it, when he might as well dispatch him at once.