What did lieutenant Cross mean when he thought that Martha belonged in a world that was not quite real?

Answer:He means that Martha's world of her youthfulness and poetry can not be compared to the world to which the narrator belongs which is the world of war so there is a distinct between these two worlds; they are opposite to each other.

His world has had most things taken away from it during war (because most things get destroyed when there is war whether it is grass, building and other things that make up the place) hence he can't relate to her world because it looks unreal to him.

All he has experienced is chaos, demolitions and death of even his own soldier friends.