Jesus told us the purpose ...Im pretty sure the rising of Lazarus has nothing to do with the free will or God's will debate. For either side.
John 11:41-42 Then they took away the stone from the place where the dead was laid. And Jesus lifted up his eyes, and said, Father, I thank thee that thou hast heard me. And I knew that thou hearest me always: but because of the people which stand by I said it, that they may believe that thou hast sent me.
We have a tendency to read into Scripture something the Author of Scripture never intended ... then use what we "read into Scripture" as some sort of proof text to support a claim.
I believe Jesus raised Lazarus from the dead shortly before His crucifixion and resurrection ... when Jesus rose from the dead, they would remember that He had also raised Lazarus from the dead, so they knew He could do it – this would shore up their faith and they would believe God sent Him ... and they would not fall victim to the lying pharisees who bribed Roman soldiers to claim the disciples had come and taken Him (Matt 28:12-15).
.