Seneca’s suicide began to falter. Blood did not ow fast enough from his aged body, even after he had cut the veins in his ankles and behind his knees. So in a self-conscious echo of the death in Athens 464 years previously, Seneca asked his doctor to prepare a cup of hemlock.
It refers to the death of Socrates in 399 BC. He died of a cup of hemlock.
Look at https://en.wikipedia.org/wiki/Socrates for a full account.
Both deaths followed legal condemnation and Seneca would have been aware of this so was conscious of the similarity in circumstances that applied to Socrates and to himself, hence the reference to self-conscious echo.