It’s a hard problem. …
If you let players use LL when they really care about the battle, and force them to roll regular dice the rest of the time, then that keeps the game moving at a reasonable speed without leaving you feeling like you lost the whole game because the dice went against you in one crucial battle.
Sure, if you save one of your precious 3 LL dice chips for that key battle, you might not have such remorse.
Also, what if the game goes 15 rounds? Is 3 really enough? Perhaps start with 3 and get an additional LL battle every 3rd round?
Allot comes down to a players level of comfort when allowing randomness into the game. Some players love the gamble, the long shot, the chance that we might still have a shot to win with some luck on our side in this last ditch effort.
Other players might become dismayed when the above scenario happens to them after all their well executed plans have them at a 99% chance of winning and feel that the dice has stolen their victory.
This is a grey area, there is no right or wrong when it comes to what is the proper level of randomness in a game of A&A?