This is something of a guess, but I wonder if this is one of the Dragon Nimbus novels by Irene Radford.
The Glass Dragon
In a realm that has always been protected by its magicians, a kingdom whose ruler's life and power is inextricably linked with that of the dragons, a time of crisis has arrived. Someone is killing the dragons, and as their numbers diminish, magic is fading from the kingdom of Coronnan. The kingdom's unlikely saviors are a young wizard whose magic is completely unorthodox and an equally young witchwoman who has been befriended by the last of the dragons.
The Perfect Princess
Though rogue magic has long been banned in Coronnan, the loss of dragon magic has opened the way for masters of these forbidden spells to wreak havoc on the kingdom. Only if Prince Darville can tame the forces of magic and rescue the spell-trapped princess who is fated to be his bride, does he have any chance to save crown, kingdom, and dragons.
The Loneliest Magician
As war rages between the armies of Coronnan and SeLenicca, an equally desperate campaign is being fought between the Commune, which uses dragon magic, and the coven, which draws its power from an older, darker source. The only hope of saving Coronnan, the king, and the Commune lies in finding the dragons and bringing them back. A young orphan is being called by the dragons, lured with the promise of discovering his true identity. Can an untested youth venture into the heart of the enemy's stronghold and find the means to set the dragons free?
I have this omnibus edition of the the first three novels, though it's been a long time since I read it and I don't remember that much about it. However it does have blue ley lines (that exact phrase is frequently used in the novels) that are lines of power associated with dragons. The first book was published in 1994 so it matches your time frame.
If I have got the correct book then the young man is a kitchen boy who has no name - he is just called Boy throughout the book. His tutor is a magician called Baamin. It is Boy who finds the blue ley lines and shows the other magicians how to use them.