Luminous Temple of Time question

Looks like it'll be a while until you finish then. It sort of gets annoying at the "collecting 100 black fragment" part.

That's after you have access to Lania's house again.

You need to collect all the Augury's and then I think you should be really close to having access to Lania's house again. I think she came back for me right after I had job changed (I had been doing the quests as I went) and after I made the Barrier Stone (after the Sentrybot, and after enlisting Agent O), you should have natural access. It's not too tedious since you get warped everywhere by Vieren.