Here's a way to activate the Lycaeum. You'll have to enter PK mode but don't worry, you'll be completely safe. You won't need to leave the Safe Zone and you can turn PK back off as soon as you're done.
The method was discovered by Veneir: Click for the post! But I wanted to make a video for it in case it was confusing for some.
Well, now you might as well run the instance since you'll be in PK...unless you're lazy like me and AFK anyway.