Satellite tournament #1 for CIS-2016 in St. Petersburg.

I have a question: all other things being equal, if blue always attacks, does that mean they get the first turn, which would be a good bonus for them?

In certain battles, it will be, and in others, it won't. For example, if you can position yourself tactically and use oil/ghost to gain an advantage, then it will be. But if the battle is slow-paced, with a focus on turn order, then it won't make a difference.

You could try to implement a system where the player with more time remaining on the timer attacks first.

By the way, you don't even need a lift – just two separate planes that are not connected to each other. When the deadline arrives, the two most powerful heroes (or the two heroes with the strongest army) are selected, and the battle begins automatically.