‘Consider, answer me, O YHWH my God:
Lighten my eyes, lest I sleep the sleep of death;
Lest my enemy say, I have prevailed against him;
Lest my adversaries rejoice when I am moved.
Yet the situation is getting desperate. He pleads for YHWH to consider his case and deal with it. He is very much aware that death may not be far away, so the situation is serious. And he prays that his enemy might not triumph over him simply because he himself is in despair and becomes careless or uncaring. He does not want him to be able to gloat over his removal. This could again well fit David's problems with Saul. But it could also have in mind any continual dangerous threat against a ruler.
‘Consider, answer me.' He urgently presses YHWH to look at the situation, and respond. Let him no longer forget him and hide His face from him. For it is a genuine response that he desires, not just comfort.
‘Lighten my eyes, lest I sleep the sleep of death.' The light in the eye can reveal the situation of the soul. He is weary of what he is facing. He feels that life is going from him. He wants YHWH to lift him from his state of resignation and imbue him with life, (which indicates that he already feels half dead), and to bring new light to his eyes so that he is again confident and again looks for and receives YHWH's positive response. For he does not want to die at the hand of his enemy.
Or the thought may be that he wants God's light to shine on Him, that He wants the evidence of His presence in His activity on his behalf, so as to save him from death.