I don't think LMLYD would fit Demi's voice well though. It'd be great to see Demi do a cover though.
And I still think it's Break a Sweat or some other song. Demi said in an interview when CFTS came out that she had Dr Luke on the album but then when the credits were revealed he was nowhere to be found. He must've taken back the song during that period which is long after 50 Shades came out.
Also they didn't even know CFTS would be the single a few weeks before it was released how would they know LMLYD wouldn't be the second single that far in advance?