Yes, in fact all the libanes who came to America before 1920 was considered as Syrians or "Another" Inmigrants.
Try tu Search in the Internet, you will find interesting articules about "Syrian Ancestry".Try this Search Macchine www.google.com on the Space bar put "Syrian Ancestry" SEARCH and you will be surprised about the different and there is an Interisting Article about it, "Researching your Lebanes or Syrian Ancestry" with a very usefull information.
Also you may try another Search Engines, because there are some web places from many Small Towns from Lebanon. For example i Find a Website from Tannourine, my town in Lebanon. And find the website of my Grandmother´s in Bshealeah Batroun. I can´t believe it but i find it!!
Try to Search and maybe you will find more Information about your Ancestry.