Ok, no I have gotten over Unicorn+Templar!Arthur... Wait, no I haven't but I must post this before the inspiration abandons me...
So, I was thinking, Lighting has all 5 Meister (6 if we consider he is a 2nd Level Tamer). Now, I would think, even if you are a genius, it would take more than a year to pass all 6 exams (I'm assuming that once you are a tamer, to be classified as 2nd level, you must take yet another exam).
So, from what we heard when the Rin was talking with Renzou, Bon and Konekomaru about the exorcist validation exam, it happen once a year and you don't really need to pass it on the first year (Konekomaru was planning to train for a year more), it also seems that, once you gain the approval to take part in missions, you then just take the classes that are related to your meister (or keep up with the basic classes + pick up the extra ones that relate to the meister you are aiming for.
So what if, let's say: Arthur and Yuri were the same age, entered Cram school together. They pass the exwire exam and the training camp (I'm assuming being chased by man-eating giant stone lanterns is a classical initiation ritual for exorcist).
Lighting might have 1st passed the Tamer and Aria exams, the 2nd year the Knight and Doctor, and the 3rd the Dragoon and 2nd Level Tamer and Dragoon and that's when he would have met Arthur and Yuri (who would have been in their first year).
Lighting meets Yuri who would have been training to be Tamer and Dragoon (I like to think Yukio inherited his aim from her) and since he is going for second level she picks him as a senpai and them everything escalates from there with Arthur playing chaperone for them.