I thought about making some remarks myself along that line in reply, Dondi! 
(But then I had to go do something else.)
There are several more ways to read the Dives/Lazarus parable in light of Rev 21+, but that’s a good start.
1.) The Rich Man (in Latin “Dives”, so traditionally in discussion that’s been his nickname for ease reference) is not penitent about his sins. He doesn’t even seem to acknowledge them!
2.) As you noted, he’s asking for water from the wrong place.
3.) He only wants the water to escape his punishment. He shows no signs (yet) of wanting to be freed from his sins and his sinning.
4.) His appeal to Abraham is probably based on the contemporary rabbinic understanding (actually ratified by St. Paul) that God will save all those who are children of Abraham by race (though St. Paul, following Jesus, extends that out to Gentiles “grafted into the promise”). As John the Baptist relevantly warns the Pharisees and Sadducees elsewhere in the Synoptics, they shouldn’t just rely on being “sons of Abraham” without repenting of their sins, and certainly shouldn’t give themselves airs on that ground (seeing as God can raise sons of Abraham “from these very stones”, probably intending a rabbinic double-entendre pun for pagans = stones, though also literally true one way or another!–whether the long way or the short, we have all been made from dirt as well as water, air and fire.)
5.) He isn’t treating Lazarus as being a person, but still as only (at best) a slave for his convenience.
6.) Moreover, Dives treats Lazarus as a slave whom he thinks nothing of expecting to walk through the fire to be tormented like himself (so far as he understands the fire)!
In other words, he’s most likely appealing to Abraham on the ground of being (but only merely) a son of Abraham, yet he isn’t willing to treat Lazarus with the same dignity due to a son of Abraham: as Dives can easily see for himself that Lazarus must be!
7.) The gap between them cannot be like having them separated in some pocket dimension; otherwise we would have the notion of Dives being completely separated from communion with God, but not entirely separated from communion with Abraham!
8.) Dives ought to have been not only asking for the true water of life, but he should have been cooperating with the consuming fire, i.e. the Holy Spirit the one and only unquenchable and everlasting fire, our God. He’s still defying the fire, thus still (even literally in several ways) sinning against the Holy Spirit. And he wants Abraham and Lazarus to join him in acting in defiance against the fire.
(This is probably the spiritual meaning of the great chasm they cannot cross even if they wanted to.)
Asking for even the river of life (i.e Christ) in order to merely escape the fire (i.e. the Holy Spirit), is to seek some kind of schism in the unity of God as well (and worse, to do so for one’s own benefit). The Holy Spirit encourages those outside the New Jerusalem after the lake of fire judgment to quench their thirst, wash their robes, enter the city and eat of the tree of life; but it isn’t so that they can escape the fire. Rather they will be baptized in Spirit Who is the fire, and so (in RevJohn imagery) they will never need light for God Himself will be their light.
