Emery's heart was stirred upon hearing about the planned attack on the Lioness convoy. During his time fighting to represent the Lioness, he had grown close with the other squires and, if he didn't leave them to look for Morgana, he would be there with them.
It was also supposed to be his duty to protect that convoy. If anything bad happened to them while he was not there, it would somehow be under his conscience.
There was also the matter of the princess' safety…
His heart started beating fast as soon as he heard the news from the knight. If it were up to him, he wished he could just rush over to help, but he couldn't afford any mistake now. If Arthur found out that the wizard Merlin quickly took off to rescue the Lioness princess, more questions would be raised and from then on, his every movement would be even more scrutinized.
He needed to do it right, hence he thought for a moment for the best course of action.