The region of the playstation doesn't matter. The region lock is between the game and the DLC.
It's easy: for the DLC to work, the Game and the DLC need to be from the same region.
Example:
US Account, Region 2 game & Region 2 DLC = DLC will work (You need to buy the DLC from a Region 2 account)
US Account, Region 2 game & Region 1 DLC = DLC will not work.
You will not be able to use a lebanese card on the US account, the way to do this is to use an Amazon account put a random US billing address and use your card to purchase DIGITAL playstation store gift card. You will receive the code instantly without getting ripped off by the lebanese middleman.
Here's the link to amazon.
https://www.amazon.com/gp/product/B004RMK4BC/ref=oh_aui_d_detailpage_o01_?ie=UTF8&psc=1