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Situation: Large American force from Detroit attacks British force at Amherstburg. The British have 2 ships in Amherstburg. The Americans have a ship in Lake Erie.
Each turn, the two British ships may roll to see if they stay docked or move out into the lake. Seeing that they will not hold the town, the British elect to roll for both ships on round one of the battle. The results are that one stays and one retreats.
Question 1: The warship that retreats is supposed to initiate a naval battle immediately since the lake to which it fled was enemy-occupied. Does "immediate" here mean before any further resolution of the Battle of Amherstburg? This is important because if the naval battle is deferred the British may gain numerical superiority.
Question 2: Is the retreating British warship the Attacker or Defender in the ensuing naval battle?
Q1. From what I understand, yes you resolve the battle immediately and then go back to the land combat. Therefore if ships escape one at a time, they fight at a disadvantage.
Q2. Section 7.1 states
A naval battle occurs when one player moves warships onto a lake (attacker) occupied by the enemy (defender).
Based on this definition, we assume the retreating British ship is actually the attacker since the Americans occupy the lake.
We played one round of simultaneous combat and then the British as the attacker in your example has first choice of retreat.