Had a thought, thanks to @emeraldphantoms !
Anyway, the train of thought was Luke has always put music first, even above his friends in many cases, and due to this he can be a little short-sighted in helping his friends (notably Alex) when they're not doing so well. This isn't to rag on Luke, it's just a very important thing to understand about him.
This makes him really great for Julie, actually.
I'll explain. Julie had people walking on eggshells around her after Rose passed away, and while she is grateful for their concern, she's tired of feeling coddled. She's tired of the oversensitivity. While Julie can arguably be considered an introvert, when she draws into herself she does more harm than good.
Music draws the best out of her. It's crystal clear the moment she sings Wake Up. She's iconic from the beginning, but we see her at near her worst in episode 1. She's had a bad day, has no time for pep talks or deep discussions, and even appears snappy to her family (even though she's really talking to the boys). Afterward, we get the sunshine and the sass and the flirting, the nose scrunches, the teamwork and excitement, etc.
Luke seems to be interested in her pretty early on, but also shows a bit of insensitivity toward her until they find an understanding. Their connection with their moms is related to their connection to music. The scene where Luke visits his parents is the pivotal moment for both of them. Julie has begun her healing journey through Luke's encouragement, and she realizes that he has his own to embark on. Since he reached out to her through music first, she returns the favor when he poofs into practice.
Finally Free and Unsaid Emily just help seal the deal for them. Instead of having another person ask her to look within herself to find peace, Luke allows Julie to channel that pain into her passion and into something that pushes her limits. Her peace is brighter, louder, and more aggressive, and he vibes with that.
Julie's own sensibility can't help but love the change in tune. Luke is an acquired taste, but he is fresh every time and once they find the right blend she is sold. They have the potential of continually and pleasantly surprising each other, and it's medicine for the world-weary soul.
Music is his first love, and since he views her as the embodiment of music, he is constantly adjusting to remain in harmony. Sometimes Julie is the one to adjust (see ep6) which just makes him a happy puppy, but his goal is always to flow with the melodies. He originally saw himself as the one carrying those melodies - not from a selfish standpoint; he sees connecting with people through music as a way to make everyone happier - and he develops a way to share that duty with her.
They are each other's rest, but more so each other's freedom.
