That Ryanair don't have anyone on the Aer Lingus board is irrelevant. Large capital purchases have to be approved by the shareholders. So, let's say Aer Lingus wanted to buy 15 Embraer 195s so offer more frequent service to UK airports than can work in an A320, Ryanair could block the purchase. It's not like they control Aer Lingus, but they can significantly influence Aer Lingus's business strategy.