Will the Earth ever be tidally locked to the Moon?
As the moon orbits Earth, tidal forces slow down the Earth's rotation by 2 milliseconds per century. Eventually, in tens of billions of years, the Earth and Moon would achieve a double tidal lock, where both are stuck with one side facing the other as they orbit the Earth-Moon barycenter. In 7.5 billion years, the Sun will expand past the Earth's current orbit, but the Earth may drift out further, preventing it from being vaporized. 

However, this is beside the point, because in about one billion years, all of Earth's water will have boiled away, meaning that there would be no more ocean tides, and thus the Earth-Moon system will likely never achieve a double tidal lock.

References:


Will the Moon ever leave Earth’s orbit? - Giles Sparrow, Space Answers
Harvesting Lunar Eccentricity? - Terry R. McConnell, Syracuse University
When Will Earth Lock to the Moon? - Fraser Cain, Universe Today
The Sun Will Eventually Engulf Earth--Maybe - David Appell, Scientific American
Distant future of the Sun and Earth revisited - K.-P. Schröder and Robert Connon Smith, MNRAS
When will Earth lose its oceans? - CNRS, Science Daily