I think "the coast of Lebanon" might be a better translation, but I don't know if there would be a different Arabic phrase for that (/saaHilu allubnaani/ maybe?), which is why they don't want it here…?
If you want the possessive, you have to omit the first article. You can't say 'the coast'. You need to say 'coast Lebanon'. Which translates to 'the coast of Lebanon'. - If I'm understanding this point correctly.