I think the reason why LY isn't part of any alliance is more that it serves one country, has next to zero connecting traffic, has never seen itself as anything more than a carrier that shuttles people to and from Israel, and probably sees very little likely financial benefit from doing so. And, as has been said, TLV is already well covered by the other alliances from all key markets in Europe and North America.

Also, can anyone really see LY investing the substantial amounts of money and resources it would take to link its systems with those of a dozen or more other airlines?