Ok, new prediction...
Leia gets the the lightsaber from Lupita's character (as seen in the trailer), and they keep it on display or in a vault. Finn sees this.
Finn being raised to hate Luke, steals it so that he can get rid of it. When he takes it, he starts hearing whispers, and as he gets closer to disposing it we hear a faint "where are you going?" or "who are you?" whisper. Finn doesn't get rid of it. / Ooooor, he steals it and their base gets invaded before he can get rid of it / Ooooooor he goes and takes it during an invasion to protect the base.
I feel like no one would just give him the lightsaber - especially if it's Luke's. Would be like a holy artifact to them.
Luke's lingering connection to Finn would be what brings him in to stop Kylo from killing him in the final confrontation, causing Kylo to retreat back to Snoke, making Snoke pissed and excited at the same time, raising the intensity for episode 8.
So if Luke is connecting to his lightsaber, why didn't he go find it instead of building a new one?
1. Making one was a trial he had to take.
2. He wanted to mark his own path considering (at the time) he was all like "there's some bad voodoo attached to this weapon"