For the Son of Man came to seek and to save the lost.
James White is a leading Calvinist voice. Here’s an article on his website (by someone else):
God is both active in election (“God chose you”) and hardening in reprobation (“God sends on them”).
As if the fact that it is God decreeing and thus performing the choosing for salvation did not make Paul’s point, he emphasizes that this gracious act was done “from the beginning.” This excludes our participation in the sovereign decree of salvation since it was ordained before we were born.
If all people were either saved or condemned in the “beginning”, then does it not follow that some people were never condemned? And if someone is “lost” is that not simply another way of saying he/she is condemned/reprobate? And are the lost not people God never intended to save? If all this is the case, then the statement in Luke that Jesus came to save the lost means Jesus came to save people he never intended to save. Which needless to say is impossible. OTOH if God does/did intend to save people who are/were lost, then Calvinists cannot use verses about people being lost as evidence that God will not try to save those people.
I should point out that the same Greek word is translated destruction and lose (in their various forms). Can any of our members who have studied Greek speak to this?