I have decided to read some Greek philosophy and chose to start with Lysistrata by Aristophanes but could not determine which translation would be truest to the original Greek version.
Some suggestions would be much appreciated.
I should not recommend Aristophanes as an introduction to Greek philosophy for reasons I'll explain in a minute.
But to address the immediate question, 'truest to the Greek original' might mean most literal or best conveying the sense and flavour of the original - and that might require quite a free translation. On balance I recommend Stephen Halliwell's Oxford translation in the World's Classics series, 1998.
May I make two suggestions ? (1) In Plato's 'Symposium' Aristophanes is represented as making a speech about the original nature of human beings : each person was twice what they are now : female joined to male, male joined to male, &c. Their power and pretensions made them over-ambitious and they were duly punished by the gods who split them apart. Each then looked for its original other half. The 'speech' has inspired both thought and talk about love ever since. Outside drama, this 'speech' (brief enough and vastly entertaining) is gentle initial reading.
Among Aristophanes' other plays, 'The Clouds', has a famous depiction of Socrates as a sophist and windbag. Now that might lead you into a consideration of the historical Socrates or the Socrates presented in Plato's dialogues. It is a mystery why Aristophanes guyed Socrates as he did.
(2) If you want to approach Greek philosophy through plays, I would suggest Sophocles' 'Oedipus Rex' ('King Oedipus') where Oedipus is shamed merely for what he does innocently and unknowingly (kill his father and marry his mother). There is no moral guilt but there is intense moral shame : we see the difference between what E.R. Dodds called a shame culture and a guilt culture. The World's Classics tr. of Sophocles would be perfectly appropriate.
It doesn't have to be either/ or. You could read Aristophanes or preferably Sophocles and one of the more accessible Platonic dialogues - I suggest 'Meno'.
The difference between a shame culture and a guilt culture is not just a matter of the sociology of morals (not that there's anything wrong with that). Nor it is just a matter of different ethical theories. It discloses different conceptions of morality : one, a shame culture, centred on what you do whether intentionally or not and on what happens to you (whether you can help it or not) and the other, a guilt culture, familiar in modern times, centred on what you do intentionally.
Hope this helps.