If you mean metal lathes, most turn both ways - forward and reverse. Forward is rotating toward the tool holder, which is typically on the operator's side. The headstock holds the spindle (the part that is powered and holds the chuck) and is on the left as you face the lathe with the tailstock is on the right. The spindle can be reversed for various operations but care must be used with a threaded spindle nose because it is possible to unscrew a chuck - not a good thing. Other types of spindle noses are locked and will not unscrew in reverse.
Wood lathes also rotate toward the operator so the knife is forced down against the tool rest when taking a cut.
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