Once you finish all of the Unicorn quest line Headmaster Merle A should give you a quest to go old town and speak to the guard there. He will send you back to Unicorn (Lady Blackthorn) and then the guard will lift the gates.
Complete all quest that involve unicorn way and you will be able to enter triton avenue and you'll gain entry to cyclops lane and firecat ally as well.
Don't worry - first, you have to get a quest from Headmaster Ambrose that tells you to talk to Sergeant Muldoon in Olde Town (I'm pretty sure this happens after you get started with the quests in Unicorn Way). He tells you to defeat Lady Blackhope, then when you report back to him he opens all three gates (Cyclops Lane, Firecat Alley, and Triton Avenue). : )
