Its not a question of the law of the sea really. The field does extend slightly into lebanese waters and they are only asking for the share that does extend to their waters. What is in question is where those sea borders are. Both sides are distorting their borders to include greater parts, for example israels declared border straddles the field exactly and parts are clearly closer to the lebanese shore than israeli shore as it is directed diagonally as opposed to perpendicular to the shores. Lebanon seem to want their share of the field that extends in their waters, but since both countries are in a defacto state of war, it will take a while to settle the children down. However, cyprus which is closest to the fields seem to be a good mediator as they have good relations with both countries and a possible 3rd party agreement could be made eventually.
It makes absoulte zero economic sense to posture militarily about this issue, because in any case the claim by lebanon is small in relation to the fields, to make those fields a target is just plain stupid.
The Israel-Lebanon seaward boundary based on LOS precepts has been calculated by the Department of State, and is classified. It likely could be obtained through FOI.