Right hand and left hand rules apply according to the type of lathe - ie, whether it is front or back turning
Most text books and CNC manuals show back turning as the standard - so when they talk about Clockwise (CW) arc direction, they are talking about a machine where tool is cutting from the back.
For a front cutting machine, the same G02 G03 codes are used in order to make the same part, however, the CW and CCW meanings are swapped (unless you are lying under the machine
)Hopefully the next picture will help show what I mean....