It depends on what you use the LSTM for.
For sequence labeling or sequence classification, the special tokens are not necessary. Although, there might be a slight benefit of informing the network of what is the beginning and the end of a sentence, especially if the initial LSMT state is fixed and learned.
For autoregressive sequence-to-sequence models, the special tokens are crucial. The beginning-of-sentence token serves as an instruction to the decoder to start decoding (it needs a very first state to predict what the next first token is). The end-of-sentence token is an instruction for the decoding algorithm to stop generating more tokens.