Answer: D. The lover's initials were carved on the tree.
Step-by-step explanation:
The modifier in the sentence makes it seem as though lovers were the ones carved on the tree instead of the initials being the ones carved on the tree.
This should be corrected to reflect that the initials were the ones carved on the tree and that they belong to the lovers. Option D gives the best option because in using the possessive ('s), it made it appear that the lovers owned the initials that were carved on the tree.