Word2Vec benefit in LSTM
You don't need word embeddings. Actually, in neural machine translation is frequent not to use them and simply train the embeddings along with the task.

Nevertheless, word embeddings work as a data augmentation technique, as you normally use a different (and much larger) dataset to train them, so they can be useful when you don't have much training data.

Therefore, the decision of using pre-trained word embeddings or not should be driven by the available data.