It will probably still be there then but Luna may well have left the solar system.
It's getting farther and farther away, isn't it?
At its current rate of retreat, the moon will be only another 60,115 miles further from the earth in 2,539,265,412 years. I could be wrong, but I doubt that this will be enough to let it break out of the earth's gravitation. Even if it were, it would certainly not leave the solar system altogether barring a major disruption by an extra-solar body (e.g., another star passing through).
Opps! Make that about 2,537,526,189 years in the future - I forgot to account for leap days. They add up...