If a construction lien is bonded via a surety bond, does the notice of lis pendens become discharged?
I think you are mixing apples and oranges here. A construction lien is a statutory right held by eligible contractors in NJ who have performed work per a written contract. A surety issues payment and performance bonds (usually for public projects) under which the surety agrees to protect the owner (obligee) from any valid claims alleged against the contractor (principal). A lis pendens is a formal written notice against a property in which an outside party asserts a claim in the ownership or title to that property.
Contractors or owners can bond mechanics lien to clear the title of the property pending resolution of the underlying dispute, but that type of bond has nothing to do with a conventional surety's payment or performance bonds. A mechanics lien is also not a valid basis for a lis pendens, because the lien claimant is just asserting that he or she improved the property - not that they gained an interest in the title.
If you are a contractor or subcontractor or supplier who filed a valid lien claim against a property, and that lien claim was subsequently set aside by a private bond, you could still pursue colelction of the lien claim. You would just need to file a lawsuit to enforce the lien claim, and simultaneously assert any other viable claims. I would recommend that you consult legal counsel to see what your options are.