The story may be a parable but it foretells of the new covenant life. I think it's ingeniously spoken by Jesus for all generations. It still gives us insight into heaven and hell.
Before Jesus' resurrection, Abraham would have been dead ("knows nothing" as the bible says) in the grave. There is no torture in death. His body was waiting for the resurrection. When Christ arose...so did Abraham.
In the story, for Abraham to be in heaven, this had to point to after Christ had risen from the dead and gone to heaven. The rich man was shown in hell, as in after the judgement.
Sometime after the resurrection of our bodies is when we receive our glorified bodies...just like Jesus did. He had to go to the Father first to receive it. As new covenant believers we will not be waiting in the grave like Abraham did. Jesus made a way for old and new covenant believers.