Her success turned out due to her ability to think laterally, and her drive and determination.
A. Her success turned out due to her ->
Incorrect form of idiom used. "turned out" is an incorrect form of idiom and changes the intended meaning of the sentence. it suggests success has turned out because of her abilities mentioned. whereas it should mean she has been successful because of her abilities.B. Her success seemed to be her ->
The sentence loses the intended meaning here. Her abilities are not her success. They are the reason for her success. Hence incorrect.C. Her success is to be due to her ->
"her success is due to her" is the correct usage that relays the intended meaning. But "is to be" is incorrectly used here. It is grammatically and logically incorrect.D. Her success turned out to be due to her ->
This corrects the error in A. Her success turned out to be because of her abilities. It reflects the exact meaning the sentence tries to convey.E. Her success appeared to her ->
It changes the intended meaning. It means that her success appeared in front of her abilities. As if her abilities saw her success. Hence incorrectTherefore, D is the correct answer.