Well, here we go then.
Bill: You better start tal-
Me: Officers, Bill, let me explain...
Regardless of whether or not Alicia was Lucy's friend, Lucy had plotted to kill Alicia all along for some sick reason. She hung a rope from the room above Alicia's and threw it down to the ground. When Alicia let Lucy in normally, Lucy backstabbed her (literally), killing her in the process and then locked the door from the inside, using the rope hung earlier to climb down to safety. She entered the building normally and probably removed the rope from that room later on before Howard could see it the next day.
Lucy faced her suicide - Howard was probably too scared to deal with whatever threat Lucy was holding against him, despite Howard telling us that she was dead after checking her pulse earlier with a fake knife embedded in her chest. While Bill left to get some help, Charlie must have forgotten his room key, because by the time both Charlie and Howard left to their rooms, Lucy was already plotted to get rid of us all in some way or another. She forced Howard to commit suicide by hanging, and then locked the inside of his room with a key, taking his Master Key in the process, and then leaving the room through a secret passage.
Since Charlie forgot his room key, she got Charlie's room key, unlocked that door, and killed him next, leaving the room key in that room and relocking that room with the Master Key. I was stuck the entire time in the basement, and she threw the Master Key underneath the door, attempting to incriminate me, but I assure you, she was the one behind all of this.
...and now, Lucy is the one lying on the sofa in the damn living room! She snuck into that room from a secret passage, and locked it from the inside normally/with her room key!