Regarding sale of the building, keep your eyes on ACRIS for any new data entries.
If the owner is known to be a liar, non of his claims should be taken at face value. The building may be sold, or the LL may have a motive(s) to lie about it in order to manipulate tenant(s)' perceptions and behavior. Of course, do not pay any monies or sign any documents to/with anyone other than the owner until such a time as you have verifiable proof of new ownership.
When my building was sold, no one was aware of it until we received a letter from the new owner.
I'm not aware of an instance where the owner can undertake a 'gut renovation' of an entire building unless there's seriously hazardous structural defects and the LL is required by law to correct them.
Further, any 'gut renovation' that's planned would have to gain approval from DOB and as with any repair, renovation, or construction plan necessitating a DOB permit to an occupied residential building, it would also require a Tenant Protection Plan ('TPP', aka Tenant Safety Plan) stating how any work will impact the tenants(s) health, safety, and comfort (for ex. dust, noise, ingress/egress, fire safety, etc., etc.) and what measures will be implemented to address this. If proposed work would require a tenant's relocation, then an attorney would draft a relocation agreement with ironclad safeguards protecting all the tenant's RS rights, prevent changes to the layout of the apartment, as well as (usually) providing free rent plus alternate free accommodations for the entire duration of the construction term, and a method of verifying/inspecting when the work is safely completed, oftentimes with a fixed completion date and monetary penalties awarded to the tenant for each day past the deadline that the work remains incomplete as an incentive for the owner to abide by the schedule and protection for the tenant from a LL that might wish to prolong the work as an harassment tactic.
What sort of neighborhood is your building in? Is it gentrified? Is it undergoing gentrification and if so, what stage is it in the gentrification?