Just level lancer to 30 and you can do the dragoon job quest thing. And no other classes are required because, as I understand it, when you choose to take on a job it will only use abilities from the first job (lancer) and the upgrade (dragoon). You sort of give up the ability to mix and match abiilites of other classes when you take on a job.
Go to Gridania Lancer's Guild (Wailing Barracks) and speak to Haurtefert. Select Eye of the Dragon Quest. You must also have Pugilist level 15 to activate the quest. Go to Coerthas, to the Gates of Judgement by Camp Dragonhead. Speak to Alberic a for quest details. Go to Camp Nine Ivies and head to (45-29) where you will see an exclamation mark by the little stream there. Then return to Alberic to complete the quest.
I soloed this as a level 38 THM with mostly CNJ abilities.
Edit: Forgot the fight; you have one level 35 crab and 3 fish to fight. They're much more difficult than normal level 35 mobs.