Might this rather be the meaning of "child" in Luke, as in "child of the Devil"?
I doubt it. The whole conversation is rather civil despite the extreme circumstance. There is no hint of sarcasm. The rich man calls Abraham "father" 3 times.
19“There was a rich man who was clothed in purple and fine linen and who feasted sumptuously every day. 20And at his gate was laid a poor man named Lazarus, covered with sores, 21who desired to be fed with what fell from the rich man’s table. Moreover, even the dogs came and licked his sores. 22The poor man died and was carried by the angels to Abraham’s side.f The rich man also died and was buried, 23and in Hades, being in torment, he lifted up his eyes and saw Abraham far off and Lazarus at his side. 24And he called out, ‘Father Abraham, have mercy on me, and send Lazarus to dip the end of his finger in water and cool my tongue, for I am in anguish in this flame.’ 25But Abraham said, ‘Child, remember that you in your lifetime received your good things, and Lazarus in like manner bad things; but now he is comforted here, and you are in anguish. 26And besides all this, between us and you a great chasm has been fixed, in order that those who would pass from here to you may not be able, and none may cross from there to us.’ 27And he said, ‘Then I beg you, father, to send him to my father’s house— 28for I have five brothers—so that he may warn them, lest they also come into this place of torment.’ 29But Abraham said, ‘They have Moses and the Prophets; let them hear them.’ 30And he said, ‘No, father Abraham, but if someone goes to them from the dead, they will repent.’ 31He said to him, ‘If they do not hear Moses and the Prophets, neither will they be convinced if someone should rise from the dead.’”
It is a sad conversation. The rich man feels bad and begs for mercy. He calls Abraham "father". In response, Abraham calls him "child" and explains to him that there is nothing more he can do due to the difficult circumstance.
Why did “Abraham” call the rich man “child” in Luke 16:25?
Abraham sees the suffering of the rich man who begs for some form of mercy. He has pity on him and calls him "child" in a tender manner. Unfortunately, there is nothing more he can do for him.