1) Can God willingly lie? His will is free right?
Strawman! Free will is not "free" of all restraint! God cannot deny himself, so he is not free to lie! That is why it is impossible!
2) Scripture says no such thing.
Scripture demonstrates the fact of man's choice independent of God's determination throughout Gen 2.
3) So Acts 4 is the exception to the rule? How do you know that?
The point is that the description of Acts 4 is very specific to a particular event. You cannot extend the argument beyond the context without serious logical fallacies. All arguments can only be theoretical, not absolute in nature.
4) Independent of what? God's providence and sovereignty?
Not independent of God's sovereignty, rather because of God's sovereignty. God sovereignly chose to give such freedom when he chose to give the Imago Dei.