I do not have much experience with the Lynbrook area. But a few of my clients have purchased homes on Long Island with pools. When we contacted the local assesors office, my buyers were told that if they remove the inground pool it will reduce the property taxes. The amount that it reduces the taxes is obviously different from one area/town to the next. If you are working with an agent, I would suggest you ask them their professional opinion on this area or even call the local township to find out approximately how much you annual taxes would be reduced by.
If you decided to remove it, it may become very costly, if you have a property you are interested and you have an inspection done, you may also ask the home inspector their professional opinion to have this removed. There are different types of pool. In the two transactions with my clients, they ended up purchasing the homes and fell in love with the pools.
Good luck. If you have any questions, please do not hesistate to ask. I would be happy to assist you.
Licensed Real Estate Agent
1408 White Plains Road
Bronx, NY 10462