You should try searching www.ellisisland.org for information on arrivals.Try different members of your family and check the original ship's manifest to see what they declared as final destination (sometimes there are names of relatives). Don't forget to be "creative" with the spelling...
There's a Joseph Ecy who arrived in 1914, as an American citizen.
There's a Hanna (John) Fahid who arrived on 30 November 1894 with the "Obdam" ship from Rotterdam/Boulogne.He was 32 years old, from Syria.
Remember that since Lebanon did not exist, most (future Lebanese) immigrants around that time declared "Turkey" or "Syria" as their home countries.