To worry.

During the akuma raid in the Rewinding town, Lenalee and Allen tried their best to fight the akumas. However, the akumas were stronger than they expected. Allen was taken down first. Lenalee fought alone to protect Allen, however they beat her.

When Allen finally came to, he was in a room he couldn't recognize. Miranda was there with her hands attached (read: stabbed) to the clock. The Akuma stabbed Allen's Innocence to a wall as well, so he couldn't move. Allen then heard someone talking: "An exorcist doll is rare." And there, he saw unconscious Lenalee looking pretty and all dressed up.

Allen: "Lenalee!"
Akuma: "Watch what you say, she is Miss Road's doll now."
Akuma: "She fought desperately to protect you."

Okay, long story short, Allen released his arm due to his rage of the Noah family being humans who kill other humans. Road stabbed Allen's left eye—sadistic much, I know. He still tried to fight the akumas with all those injuries. He managed to release Miranda, but he started to lose his consciousness again. Scared Miranda tried to protect him from the attacking akumas, and... somehow, her clock reacted. It created some kind of sealed space around them, and Allen's wounds disappeared; even his ripped clothes turned back to be the way it was.

With his Innocence, Allen grabbed Lenalee into the space created by the Clock. He was relieved knowing that Lenalee was still alive. Allen assumed that the Akuma caused her getting some nerve paralysis. A few moments later, Lenalee regained her consciousness. Allen told them that they were saved by Miranda's Innocence, and thanked her for that. Allen's gratitude really moved Miranda.

While there didn’t seem to be any importance in these moments, I believe that the way Allen worried about Lenalee, and how Lenalee fought akumas alone to protect the numb Allen, was already a progress for them to become closer friends. They already started to care about each other—because Lenalee was a comrade to Allen, and vice versa. When you become friends with someone, you would care about what happen to them, and worry if they get hurt.