Good Luck is the best way to get to the airport from the LES.
I have had a couple issues with airport pick-up from JFK but mostly they are really a fantastic service and I would highly recommend. It's nicer and cheaper than taking a taxi. As with any pick-up service I would just tell the driver to be there 15 mins before you think you really need to leave just in case!!!
Our driver arrived on time and was extremely friendly and helpful and the limo was beautiful. Overall our experience was outstanding and I would definitely recommend Limo Services to anyone and will call them if we need a limo in the future.