The correct option is D NO CHANGE
A clause that is dependent on another clause for its full meaning, is called the subordinate clause (Her friends accompanied her) that's dependent on the main clause (Lina was willing to go to the theater). The given subordinate clause is the condition on which Lina would go to the theater, hence the sentence is condition-related. 'If' is the conjunction used for condition-related sentences, it's appropriate as it completes the meaning of the sentence, hence it's correct and option D is correct. 'Though' is a conjunction used for sentences that are contrast in meaning, example, "Lina wanted to go, though her friends didn't." Since that isn't the case here, option A is incorrect. Option B is incorrect, 'as' is used for cause-related sentences, where the subordinate clause is the cause. Since the subordinate clause here is a condition and not a cause, option B is incorrect. 'Should' and 'if' are slightly similar in meaning, when 'if' is replaced by 'should', the grammatical structure of the clause after it should also be changed, example, "should her friends accompany her". As changing the clause itself is not an option, C is incorrect.