Why I get a very low accuracy with LSTM and pretrained word2vec?
Its huge discrepancy, I suspect a lie.

While +33% can be achieved, you said that you tried very different architectures and you did not get even close. Dont expect that one tweak, one layer, one xyz can give you all of a suddenly such a huge increase. If you did not get closer using suggestions from the paper there is also a possibility (not saying they did, but it has been done before in ML papers- lying about accuracy achieved without providing code) that they lied.