Nope. Jesus was not giving a "parable of prayers to the dead" in Luke 16 with the story of Lazarus and the rich man
The details state otherwise
as of vs 22 - the rich man is dead. and so also the poor man
22 So it was that the beggar died, and was carried by the angels to Abraham’s bosom. The rich man also died and was buried. 23 And being in torments in Hades, he lifted up his eyes and saw Abraham afar off, and Lazarus in his bosom.
So now we have 2 dead people - the rich man and the poor man as of vs 22
the dead rich man sees Abraham, and also sees Lazarus in Abraham's lap
24 “Then he (the rich man) cried and said, ‘Father Abraham, have mercy on me, and send Lazarus that he may dip the tip of his finger in water and cool my tongue; for I am tormented in this flame.’
As R.C. Sproul notes - this is a prayer to Abraham , a request of the dead, it is not a pray to God.
25 But Abraham said, ‘Son, remember that in your lifetime you received your good things, and likewise Lazarus evil things; but now he is comforted and you are tormented.
In that section above - we see that the rich man is asked to remember his LIFETIME - the days prior -- when he was ALIVE. When he LIVED.
26 And besides all this, between us and you there is a great gulf fixed, so that those who want to pass from here to you cannot, nor can those from there pass to us.’
27 “Then he said, ‘I beg you therefore, father, that you would send him to my father’s house, 28 for I have five brothers, that he may testify to them, lest they also come to this place of torment.’ 29 Abraham said to him, ‘They have Moses and the prophets; let them hear them.’
30 And he said, ‘No, father Abraham; but if one goes to them from the dead, they will repent.’ 31 But he said to him, ‘If they do not hear Moses and the prophets, neither will they be persuaded though one rise from the dead.’ ”
In that section above we see the reader reminded that we are talking about "The DEAD" and someone going to the living "FROM the DEAD"
And apparently it is Abraham alone that determines if he will send someone or not. in this parable.
Jesus was giving a testimony of what Paradise is like;
Jesus never says the rich man went to paradise.
No text says anyone suffers anything at all in paradise.
Instead what we see is
2 Cor 12 - Paradise is in the third heaven
Rev 2- where the tree of life and the throne of God is - Rev 22:1-3
it includes 2 sections divided by a great fixed gulf
IN the parable Abraham never says that the rich man is in paradise all he says is that between Lazarus who is in Abraham's lap in Paradise -- and the rich man who is in Hades not paradise, who is in torment not in paradise - there is a great gulf.