Will the Earth ever be tidally locked to the Moon? From my basic understating, 

Momentum is being transfered from the Earth's rotation to the Moon's orbit by tidal friction. The Earth's rotation slows down and the Moon receedes from the Earth as it moves into a higher orbit. This will continue until the Earth's rotational period is equal to the orbital period of the Moon, i.e the Earth is tidally locked to the Moon.

Assuming I have the above correct - and please correct me if I don't - will there, realistically, be enough time for tidal locking to  occur before the sun expands and engulfs the Earth? Or is there another reason the Earth will never be locked towards 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