What types of lawsuit settlements are exempt from bankruptcy turnover?

I don't know what invasion of privacy has to do with anything you described, but what is exempt and what is not depends entirely on the applicable exemptions that were available to you and employed when and where you filed.

Exemptions vary widely from state to state and no attorney is going to know the exemptions in all 50 states. So I am attaching a chart that lists in non-legal terms the exemptions from all of the states. Unless the laws specifically provide for an exemption, it is within the discretion of the bankruptcy trustee whether or not to demand the turnover of any individual asset. Hope this perspective helps!

You should have included the lawsuit as an asset on your Schedule B. Other than that, as Ms. Bunce pointed out, exemptions vary wildly by state. You should talk to a bankruptcy attorney to see what you could exempt. A link to Alabama's exemption is below.