Question: If Christ took upon Himself the grave and the Lake of Fire, then there is no need of repentance and trusting Him for our salvation. Wouldn't both penalties be paid in full?
Response: We could not be saved unless Christ paid in full the penalty demanded by God's judgment against our sin. The penalty of sin is death. That is the sentence. Death has already passed upon man and will culminate in his separation from his body and from this planet and from God forever unless he can be justly forgiven. God cannot merely make a bookkeeping entry in heaven. The debt demanded by His justice must be paid in full for man to be pardoned. Calvinism says that He paid the full penalty only for the elect, but the Bible repeatedly says it was for the whole world (Jn:3:16; 1 Jn:2:2, etc).
Why do we need to repent and believe in Christ if the penalty has been paid in full for everyone? The good news of the gospel is that salvation is offered to all. That offer requires acceptance on man's part. God does not force His love and grace upon anyone. Even the Calvinist, though denying any volition on man's part, acknowledges that the offer must be accepted through the work of God's grace.
There is no hint that sin's penalty for individuals can be isolated from the whole or that Christ paid for each one's sins individually. Just as to break one commandment is to be guilty of breaking the entire law (Jas 2:10), so payment for one sin is necessarily payment for all.