Could there be a difference between "lift up something" and "lift back something", like:
- He lifted back his head.
- He lifted up his head.
Are these sentences different?
Yes, there is a difference.
The first is grammatically okay, but would rarely be used because a much more common expression is already widely used:
"He tilted his head back."
The second sentence is common.
"lift back" presents an awkward usage to English speakers because "lift" implies a movement in a direction other than "back." That is, "back" implies "behind", whereas "lift" implies "up." They can be used as a phrase, and the listener would deduce a diagonal motion, but it would generally be perceived as an awkward statement.