Because of the "eye dominate" factor... your opposite hand will likely change everything that you ever did with a cue stick left handed. For instance, I shoot right handed. Over the years I adjusted to a squared stance with my natural hand as I see (and feel) my lines better and my stroke is smooth and straight with good cue ball control (when I'm on).
However shooting lefty took a lot of years to figure out (and get used to), because I was always trying to mirror my natural handed shot. Now I'm shooting with a completely different stance, bend, movement, head position, ect... While I have a prominent squared stance right handed, I now shoot in a side-on stance left handed and have developed a much better game with both my shot making and my cue ball control.
I have run several racks left handed and can feel and move the cue ball almost as well as I can right handed (when I'm on). I believe that most of these two different stances developed over the years due to being "right eye dominant". Once I started to see the lines both ways, I just trained my body (and my brain) to become comfortable with each stance and the control found itself.
These days I don't even realize when I'm shooting lefty half of the time. My brain just says "switch hands" and it's become a regular part of my game.
Good luck with your own adjustments (however they work out for you).