If I remember correctly, Luke and Layton met as the good professor is one of Luke's elementary teacher. This is how I understood the statements insinuated in The Eternal Diva. Luke just became very fond of the Professor since he's an archeologist by trade and a detective by profession.
As an added trivia, Layton's character actually resembles Master Keaton - a kickass character that stars in the eponymous anime. Layton and he are pretty much the same, but Keaton's more human compared to Layton as he usually tackles the troubles of life such as wanting to be more than just a teacher/run off the mill archeologist, trying to be a good father and son, and the ocassional Macguyver moments whenever he's in a pinch during his detective stints.
Going back on topic, The Eternal Diva is a mishmash of sorts as the narration is actually set after the Curious Village (though a lot of cameos from The Diabolical Box are present) but the narrated story is set way before as Luke's just started his role as "Professor Layton's Apprentice."
Of course, I could be off on a few things about The Eternal Diva as it's been awhile since I've watched it. Great movie, just wish that there were more viewer involved puzzles. It initially started as a very engaging and interactive movie then proceeded to become a usual affair where you just watch and see the plot unfold. Not bad by any mean, but I kinda expected it be a Layton trademark where the story is peppered with a lot of fun puzzles.