It is locked with a Novice Lock now, and does not require a key unlock or for you to finish the quest.
And best of all it lets you go back inside.
This does not fix any bugs with the "Chasing Echoes" Quest.
"Chasing Echoes" Quest, Command Fixes
If Serana just walks around saying "we are getting close I am sure of it", and you are in Valerica's laboratory use:
setstage DLC1VQ04 35
If you are in Valerica's laboratory and she is not asking you to get "Valerica's Journal" use:
setstage DLC1VQ04 50
These may not be the same commands that you need to fix the quest but they were what i needed.
Hope this helps.