The entity, “a rock so big He can’t lift it,” implies that there is a threshold of magnitude whereby God is unable to lift things. If we specify in advance that no such threshold exists, then the entity in question is ill-defined. In other words, the phrase “a rock so big He can’t lift it” is just incoherent nonsense. So too is any question which includes that phrase.
You might as well ask, “Can God toad the wet sprocket?” It’s just meaningless blather.
In my experience, the most of the popular arguments against the existence of God are either indefensible or else aimed at the wrong target, e.g. a particular theological doctrine, as opposed to God’s existence or nonexistence. The free will argument is an example of the latter. Now, I would go so far as to deny the very coherence of libertarian free will as a concept at all, much less one which is compatible with divine sovereignty. But this isn’t an argument against the existence of God. It’s just an argument for compatibilism, which may possibly be extended into a moral objection to God’s alleged behavior. And that moral objection doesn’t challenge God’s existence at all. Indeed, it too has at least one possible answer.
In my judgment, the problem with theism is not that it can be proved false. On the contrary, many forms of theism seem perfectly consistent, internally. Rather, my biggest issue with theism is that it is not demonstrably true. That is, it lacks sufficient supporting evidence or other rational warrant. As long as that remains to be the case, I am quite satisfied to deny theism.