Upvote:3
Israel does not have a policy against issuance of visas to Lebanese. Such visas require confirmation from the Israeli Government, unlike an Armenian passport, which can be done at the Embassy level. I have no idea if the "Lebanese" entry on your Jordanian residence permit, which the Embassy probably see when they ask why you are applying from Jordan and not Armenia, will require the referral back to Jerusalem. Even if it does, however, there is no reason to think that your application will be rejected.
Not only does Lebanon have a policy not to issue a visa in an Israeli passport, I believe it is also a crime to visit Israel on a Lebanese passport. You should investigate whether your visit would leave you liable to arrest in Lebanon, should you ever go there, even if you visited on your Armenian passport.
EDIT: Probably worth adding, so as not to make Lebanon look unusual, that holders of Israeli passports may be prosecuted for visiting Lebanon without a special permit, independent of whether the Lebanese would admit them (for example, if they entered Lebanon using another passport based on dual citizenship).