You're likely going to get some questions from security if you're in the line with him for his AF flight, but if you speak Hebrew and are able to converse with the security and explain you shouldn't have a problem going through. I've never tried it on BA, but have arrived way early for El Al flights in the past and did the exact same thing.

The Dan lounge is another story. Without the invite from the checkin desk I don't think you're going to be able to get in. Is your OH flying in a premium cabin? You can likely get them to allow him a guest.

That being said, you aren't really missing much if you can't get in to the Dan Lounge. Do you have an Israeli Platinum CC? A lot of those will give you the option to enter, or sometimes paying with some "stars." Priority pass also works there IIRC. I think Diners club too.