O.K:
To speak to this argument.....it helps neither the Calvinist nor the non-Calvinist:
The "Why do you pray" thingy.....is a dead-end for both groups.
The arguments line up somewhat thusly:
I.) Why does a Calvinist pray for the lost??
Inasmuch as God has, of his own free will and purposes surely ordained all of those who will believe, and insomuch as those who are chosen have their sins assuredly atoned for upon the cross, it is pointless to ask God to retroactively consign his beloved Son to pay for sins for which he did not atone.
All those whom God has elected have already had their sins so expiated or atoned for and propitiated, that the Arminian could (reasonably) argue that it is an exercise in futility for any Calvinist to pray for the lost.
After all, if God has chosen that person and they are "elect"...than, prayers are unnecessary inasmuch as it is a surety that they will (in God's own perfect timing) come to salvation by grace and be regenerated.
If, however, that person is not of the elect....than to pray for their salvation....is in fact to pray for the very converse of God's perfect will....it is to "kick against the pricks".
If God has chosen, of his own inscrutable and perfect purposes not to elect that individual, nor to atone for their sin, for his own glory, than to wish for or pray for their salvation is to find oneself to fight against God....
If they are of the elect, than their election is assured and no post-facto prayers will make any difference, or they will, at best find themselves to be at variance with God's perfect will.....
That's the argument the non-Calvinist could make: