Sorry, are you talking about reversing the positions of the headstock and tailstock or standing on the wrongs side of the lathe and reversing the lathe direction.
Firstly, Being left handed is only an issue when bowl turning, spindle turning can be either handed or as me, ambidextrous. My teacher made me turn left handed (I did not know) until I could do it, then let me turn right handed. Now I'm happy turning with either hand.
Truthfully, if you are just learning, keep things as they are and turn right handed, yes it sounds wrong, but you are learning a new skill and your body has no reference, so will adapt quite readily to using your hands that way.