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.
"Lifted back" implies that he ended looking straight up, while "lifted up" implies he started looking down, and is now looking ahead.
"Lift up" is not grammatically correct. It is the same as raise up an object. To lift is to raise and there is no need for the "up"