This parable does not have those implications.
Pray can simply mean asking in the natural sense, such as, “I pray, sir, could you tell me how to get to such and such?” It’s antiquated in English, however but is found used that way in older Bible translations. It does not mean “prayer” as we understand “Lord, teach us to pray,” as the disciples asked Jesus.
Prayer in the biblical sense means people in this world asking those outside this world, in the invisible spiritual realm, for things, and the Bible teaches that we are only to pray to Living God, not other created beings. Angels certainly appear to bring prayers to God like messengers, but they aren’t shown to have the authority to answer them themselves.
In this parable, the rich man is no longer in this world and addressing Abraham, but with him in the afterlife although there is an impassable gulf between them. So the rich man isn’t praying to him, but talking to him. And it’s natural he would. He is an unbeliever, and he knows by Cont’d