Final answer:
The correct answer is D) Lilly went to the store to buy eggs for her mother, as it is the only option that forms a complete thought with a subject and a verb and can thus stand alone as a sentence, making it an independent clause.
Step-by-step explanation:
An independent clause is a group of words that contains a subject and verb and can stand alone as a complete thought or sentence. However, a dependent clause cannot stand alone and needs an independent clause to complete its meaning. In the question, 'Which of the following is an independent clause? A) Because David had a large soda. B) When it rains tomorrow. C) Since you were out late. D) Lilly went to the store to buy eggs for her mother.', the answer is D) Lilly went to the store to buy eggs for her mother. This is because it contains a subject ('Lilly') and a verb ('went') and expresses a complete thought, hence it can stand alone as a sentence.
To further clarify, options A, B, and C are examples of dependent clauses. They start with subordinating conjunctions ('because', 'when', and 'since') and do not form complete thoughts on their own. Each of them lacks the capability to be a complete sentence without being attached to an independent clause. This is also why they are not suitable as answers to the question regarding independent clauses.