John Gill Commentary Job 16:5

"[But] I would strengthen you with my mouth, And the solace of my lips would assuage [your grief]." — Job 16:5 (ASV)

[But] I would strengthen you with my mouth
Comfort them with the words of his mouth; so God strengthens his people with strength in their souls, when he answers them with good and comfortable words; an angel strengthened Christ as man when in an agony, comforting him, suggesting comfortable things to him; so one saint may strengthen and comfort another when in distress, whether of soul or body; see (Psalms 138:3) (Luke 22:43Luke 22:32) ;

and thus Job had strengthened and comforted others, with his words in former times, as Eliphaz himself owns, (Job 4:3Job 4:4) and so he would again, were there a change in his circumstances, and objects presented:

and the moving of my lips should assuage [your grief] :
words uttered by him, which are done by the moving of the lips, should be such as would have a tendency to allay grief, to stop, restrain, forbid, and lessen sorrow; at least that it might not break out in an extravagant way, and exceed bounds, and that his friends might not be swallowed up with overmuch sorrow.