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?

• @zephyr One paper says that about 2.55 Gyr from now the sun will reach its maximum $T_{eff}$. 5.42 Gyr from now the sun will be 37 percent larger than today, which still keeps it quite far from Earth's present orbit. 7.59 Gyr from now the sun will reach the tip of its red giant expansion. This seems consistent with the Scientific American article. The paper I linked in this comment also estimates the mass loss of the Sun and finds that the Earth's orbit would expand far out enough to survive, but as a molten planet. Oct 20 '16 at 15:57