As I do a little more searching, I found this site:

http://www.cs.unimaas.nl/m.winands/loa/discussion.html

Rule 9 deal with this situation, and here is what is said about it:

Soucie did not cover this situation. LOA players thought that this situation was impossible in a real game for a long time. But computer simulations proved that such a situation could occur in a real game. The alternative proposed and commonly used was that the player has to pass. Unfortunately Soucie has died in 1997. It is hard to find a satisfying rule.

Some points against the lose rule.

* The object of the game is to connect your pieces in one group. Not to eliminate the opponent's moves like in Amazons or draughts. LOA is a connection game, you win by connecting your pieces.
* You don't know if the player would have lost the game. It deserves a chance to defend itself.
* The player is punished enough by passing. In LOA passing is mostly disadvantageous.

Some points against the passing rule.

* If you look at rule 3 a player has to move, passing is out of the question.
* The game is called Lines of Action. The name suggests active play, not passive play by passing.
* The player would probably lose the game anyway in this situation. By the passing rule the game would continue unnecessarily longer.
* It is possible that passing is an advantage. The player is not punished but rewarded.

Current Results

Recently, Jorge Gomez Arrausi posted the following alternative solution to this matter: "If a player cannot move, the game should be drawn. The objective is the connection." The problem with this rule is that introduce drawing, which is not the intention of LOA (see also the discussion about rule 8).