Premonition

She should have believed that a nightmare is an alert of an upcoming misfortune. But nothing can be done.

Just a few seconds after making up with Lenalee, Allen had this one misfortune which seperated him from the entire group. He was captured by a villager because he needed help from "the black clergymen". Later, Lavi joined him and long story short, they found a new exorcist, that is Alleister Krory III. In their journey to reunite with Lenalee and Bookman, these three met a member of Noah family named Tyki Mikk. He had his human appearance, so nobody was aware of his real identity; not even his human friends. He noticed Allen and Lavi's uniform, but he didn't do any harm to them at the moment. Allen challenged him and his human friends at Poker. Allen's game? Epic win.

On the other hand, while waiting for the three exorcists to rejoin with her and Bookman, Lenalee had a nightmare where she was all alone on top of ruins. She also saw Allen's body (...corpse?) beneath the water. The dream stopped there, and she woke up crying.

After the whole team reunited, Lenalee saw something strange on Allen's left arm, so she took a look at it—the arm was crumbling. The exorcists were surprised, but Allen made up an excuse that he must had been a little tired and he asked them not to worry since it wasn't an injury. Lavi and Bookman only displayed some curiosity, but Lenalee was different. She remembered about her nightmare and looked very worried of Allen.

Lenalee: "I've thought of this before... Allen-kun's left arm... is a little fragile, isn't it..."
Allen: "...? Lenalee?"
Lavi: "You made her cry."
Bookman: "You made her cry."
Krory: "You brought her to tears."
Allen: "Eeeehh?!"

darkness

I'm not sure when exactly did this scene happen as this was just a flashback which appeared 20+ chapters later, but obviously it was after Lenalee saw Allen's Innocence. That night, the team was resting, probably all of them were in the same room. Lenalee had the nightmare again. When she woke up, she found everyone but Allen (and Timcanpi), so she went to look for him.

When she found him, Allen was covering his left eye, and looking troubled. Lenalee noticed, but Allen stepped back and said that she could go back to sleep. Worried, Lenalee grabbed his hand.

Lenalee: "If you don't want to show your left eye... I won't look at it, so... Don't go further into darkness.."
Allen: "?"
Lenalee: (trembles) "Don't disappear into darkness...!"
Allen: "What's wrong, Lenalee? Ever since we rejoined from Krory's castle... you haven't been looking well. Did something happen? Did you have a nightmare?"
Lenalee: (cries and hugs Allen) "Uuh... Uwaaaaaaah!!"
Allen: (blushes) "!? Waaahh?!"

Allen was surprised when she suddenly hugged her, and he blindfolded Timcanpi for the sake of safety (hint: stalking older brother). Lenalee then told Allen about the nightmare. She was very worried, but she was glad Allen was alright. Allen patted Lenalee on her back and said that she was being overprotective. Lenalee finally smiled and apologized.

Allen then asked her the reason why she seemed to care so much about her comrades while Lenalee was still in his arms. "It seems that you're only fighting to protect us." He probably asked because of he'd been seeing Lenalee protecting and worrying about her friends a lot... namely Allen himself.

Lenalee: "When you close your eyes and think of the World.... what do you see? I don't see a world like a map. I've been in the war for a really long time... What I see is the faces of my comrades under the Black Order. My friends are more important than the real world. To me, the death of one companion... is like a piece of the 'World' being destroyed."

Not long after, Allen got his Innocence destroyed by Tyki Mikk. Upon seeing Allen's blood trace with no body around, Lenalee was terrified. She must have thought that he was dead. Yet that other night she just told Allen that the death of a companion equals a destroyed world. It was as though a part of her nightmare had become real. But then, a messenger from the Black Order told the team that Allen was found to be alive. He was, however, no longer an exorcist because of the loss. Thus, the team had to go on without him.

This prove that Lenalee's premonition was true afterall. She wasn't just being overprotective, hence the chapter in which she had the nightmare was entitled "Premonition". Indeed, maybe dreaming of a friend is not very uncommon. It might be just a dream. However, the fact that it was actually a warning for an upcoming misfortune? It shows that Lenalee and Allen is somehow connected.