I notice that your question leaves "free will" undefined, so let me propose the definition found at merriam-webster.com: "the ability to choose how to act; the ability to make choices that are not controlled by fate or God."
I presume that no one imagines that neuroscience will prove that some of our choices are controlled literally by fate or God. So if neuroscience is to show that some or all of us lack free will, neuroscience must show that some or all of us lack the ability to choose how to act or the ability to make choices.
I don't think we need neuroscience experiments to show us that some people lack free will in the sense just defined: for example, people who are in the midst of drug-induced mania or a psychotic episode. To show us something we didn't already know, neuroscience would have to show that people in general typically or routinely lack free will.
Some neuroscientists do claim to have shown that, but their arguments are woefully unpersuasive (in my judgment and in the judgment of philosophers more expert on this topic than I am). For one thing, neuroscience would have to show more than that our choices are causally determined by prior factors, because on one analysis of free will -- the analysis accepted by most philosophers, as it happens -- a free choice can (and perhaps must) be causally determined by prior factors.
For more on this topic, see Question 5733.