I have experience with windows and am happy to shed some light on the process.
1) Window replacements must be approved by LPC. They do have specific requirements, which are indeed complex and costly, but are designed to preserve the historic character of the neighborhood.
2) There is therefore a benefit to replacing the windows building-wide if that's needed/an option. It is also the most efficient option. There is an organization related to the LPC that offers financial assistance to historic buildings undertaking restoration work; it might be available to individuals as well.
3) You might be able to get away if the windows you are considering replacing are in the back and not visible from the street. For facade windows, the best course of action is to follow LPC's requirements.
LPC has been known to issue serious fines and violations to projects that aren't in compliance, even when seem minimally offensive. I would therefore recommend NOT taking this option. For that reason, sane, respectable contractors would turn down a job that's not in compliance.
4) You will need to hire an architect to prepare drawings and filings for the LPC, though sometimes contractors offer this service. Presuming that this is a co-op, the board will also need to sign off on these plans.
Hope this helps!