As tragic as the events of the 3rd trial are to Luke, it's heartwarming to see him genuinely cheer up for a moment at the prospect of helping hear the parrot's testimony. It really does seem to take his mind off things.
Seeing Professor Layton and Maya reunite with Luke and Phoenix, after their apparent deaths.
Luke:[with tears in his eyes]I'd thought I'd never see you again... Maya: YOOOOOOO NICK!
When Layton and Luke discuss Espella's relationship with her father, Layton realizes that this subject matter must weigh heavily on Luke, and tells Luke that if ever he wants to say something to the Professor, he is totally free to do so:
Professor: I'm always ready to listen, Luke.
The Like Brother and Sister relationship between Luke and Maya is very sweet indeed, especially since it's almost immediate. They get on like a cauldron on fire, and converse like they've known each other forever. Just watch them solve a puzzle together.
After Maya's apparent death at the end of "The Golden Court," Phoenix, Luke and Espella are on the run from angry townsfolk. Inquisitor Barnum finds them, apologizes for allowing Maya to die and informs them of what to do in order to escape.
During Phoenix's Heroic BSOD thanks to Maya being thrown into the fire tavern owner Rouge eventually tells him to snap out of it and challenges him to a puzzle. This, being a Professor Layton game, works.
Usually all trials in Labyrinthia end with someone being thrown into the fire. When you win the last one, though, you get the traditional "Not Guilty" message because nobody around is or ever was a witch, and for the first time, you also see the traditional confetti fall... except it's actually flower petals welcoming the new history of the city.
On a similar note, the fact that the Judge allowed Jean Greyerl to live on the grounds that she had not committed any crimes thanks to Phoenix's passionate arguing in her defense, even though she was not his client.
In addition, at the end, His Honor declared that he was actually quite relieved that none of the "witches" he had sentenced had actually been killed, and says that many of the people of Labyrinthia, himself included, would like to stay and live there, even though their memories were returning.
To drive the moment home, it should be noted that, aside the prologue case, the game's rendition of "Won the Lawsuit! ~ The First Victory" doesn't play for the witch trials...until this moment, where Wright and Layton win the last Witch Trial in the history of Labyrinthia.
In Edgeworth's cameo, he notes that he's missed hearing Phoenix's "spell" (his trademark "Objection!) while Nick was away in England. Of course, he admits this after insulting Phoenix for the best part of the scene.
Before the long chain of puzzles in Chapter 7, Luke and Layton have a conversation about Maya and Phoenix, talking about how glad they are they met and how much faith they have in the two of them, and discuss what kind of people Maya and Phoenix are. They have nothing but praise, which is a long way from their initial impression of thinking they're just plain weird:
Luke: When I was teamed up with Mr Wright, one thing became clear to me... He's definitely someone that will always do his best to help his friends!
Layton: I agree, Luke. He's a fine young lawyer with a heart of gold. I'm quite confident the trial is safe in his capable hands.
Luke: Me too! And then there's Maya... always strong and courageous! Not to mention full of energy! She's a bit reckless sometimes... but always with good intent!
Layton: We're lucky to have them on our side.
Luke: I'm really glad we met them, aren't you, Professor?
Layton: Yes, Luke, I'd certainly agree with you there. Both Mr Wright and Miss Fey are friends that can truly be relied upon.
At the end with Espella and Darklaw/Eve. Despite all of the hardships they endured, the two's friendship has rekindled. It's also a happy Tear Jerker.
Espella: (starting to cry) Eve...will you...will you still be my friend?
Eve: .........of course.
Espella: Thank you!
The image following is of a smiling Eve and Espella holding hands, while the Storyteller gives them a fatherly smile