You can redeem AA miles for LY flights. check AA.COM for more details.
The other airlines you mentioned fly to Israel themselves and have no partnership with LY. Of-course you can use their miles to travel on them or one of their other partners.


BTW, the LY experience doesn't really exist. In fact, in my opinion, especially on business class, LY is the worst airline between the US and TLV (they may have good service, depending on the crew, but worse seats compared to other airlines).