Libertarian Free will is a kind of indetermination of the will based on equally desirable objects of choice. That is, it requires that there exist at least two objects which are similarly desirable so that we can deliberate and proceed to choose between them. In cases where one object is extremely desirable and the other extremely undesirable there is no indetermination of the will and thus no libertarian free will.
Strictly speaking, libertarian free will is just the position in opposition to determinism, i.e. the inability to make a choice devoid of causes external to the will. Choices don't have to be equally desirable. And even if a choice is
undesirable, it doesn't violate libertarian free will if the choice is
available.
The problem with libertarian determinism is that neither main branch - event caused or agent caused - is intelligible if you admit that the principle of sufficient reason holds true.
In Heaven we will see God face to face, and his goodness and glory will be manifest. God is that which is supremely good and desirable, and in Heaven we will see clearly that this is so. Thus we will not choose anything over God, which means that we will not sin. Thus in the choices which regard God and God's will there will be no indetermination of the will and thus no libertarian free will. Note that the faculty has not changed, but only the clarity with which we see the objects, and especially God. Depending on your definition of free will, we will or will not have it in heaven, but since we will see God face to face we will never choose anything over him.
The problem of suffering and free will hinges on the idea that a
good god would have
necessarily created us with this desire not to "sin" from the outset, so that human caused suffering would never exist.
Whether the result of that is free will in
any sense of the term is somewhat immaterial, since it can be argued that in many cases, I myself don't have free will, even if you believe that free will exists.
For example, if I have the choice to do something terrible, say molest a child, I will, ceteris parabis,
never ever do such a thing because the idea is anathema to me. I don't consider myself a "robot", as Christians are want to suggest someone absent free will would be. I don't find myself "lessened" in any way because my conscious renders me
unable to pick certain choices. It's up to the theist to show why a person is "more of a person" than me because they may desire to do terrible things...
