My ex-wife has agreed to be bought out of my new york state pension. What paperwork is needed and do I need a lawyer

In the absence of a divorce agreement that provides otherwise, a judgment of divorce terminates the right of the ex-spouse to any share in any pension or survivor benefits of their former spouse. Assuming your divorce judgment provides that your ex gets a one-time payment as a pension buyout, this needs to be effectuated with a QDRO (Qualified Domestic Relations Order). The pension plan won't pay your ex without a QDRO, and the QDRO will only include such benefits as are found in the divorce agreement. Do you need a lawyer? I'd say "yes". Even divorce lawyers tend to need help from other lawyers who specialize in QDROs.