You can find Lily on the lower floor on stage 5.
Kill the goblin who is using Clara and grab a key he drops. You should be able to open the gate connecting to lower floor.
Thanks. I found it.
In fact, that door is located in the stage's entrance passage, so I've been ignoring it.
And the reason I've been ignoring it there is because of a previous bug where the map was cleared after every time I loaded the save, which caused me to not see or remember that there was a door there.