If I were just starting out -- not just is disc golf, but in sports in general, I'd learn to be ambi. When my youngest son, who's now 26, was just a toddler, I noticed that he'd pick things up and throw things with either hand, so I would conscientiously be sure he developed both as he played sports. It turns out that he writes left-handed (so technically a lefty) but does so many things right-handed it would help him in sports. Imagine in little league basketball the 6- or 7-yr-old kid who dribbled and handled the ball lefty dominate but used both, and then shoots righty.
In my area, we have a highly-rated grandmaster who drives both righty and lefty backhand. He actually told me the story of some 15-20 years ago when he was much younger he hurt his right arm and couldn't use it at all -- but wanted to play dg, so he taught himself to throw LHBH. UCF is correct that it drives people crazy, but getting to know him after playing on his card often over several years I've learned that he really uses his LHBH drive for long holes where it is open on the left and the hole turns right. He still has a solid RHBH anHyzer game for touch shots and wooded shots, as well as BH rollers which he only throws RHBH.
I am going to assume that when you played tennis you played lefty with a two-handed backhand. I am assuming that only for the purposes of a partial explanation and maybe something that might help. The tennis shot and the disc throw is called "backhand" because in the early days (before all the increases in technologies of both discs and racquets), if you did it correctly you would see the back of your hand on the follow-through. Recall that before overstable discs and back when all racquets were made of wood and had smaller faces, form was much more important than today. It is likely that you are comfortable with the LHFH because it's very similar to your tennis stroke. And the RHBH is very similar to a the swing of a left-handed hitter in baseball -- so still geared toward natural lefties. If you're left hand dominate these make sense and are not necessarily that unusual. I have 3 or 4 lefty friends who play and they also have some "quirk" like that. They're all predominately LHBH players. But one throws all of his overhand shots right handed and also throws RHFH; the others will throw forehands both righty and lefty depending on the touch or situation.
To throw a disc LHBH, is similar a similar arm motion to a one-handed backhand in tennis, but different footwork. Obviously in tennis you don't turn your body to hit a backhand, so here's where it gets tricky. The footwork is actually more similar to a right-handed batter's swing in baseball. So combine that footwork with the arm motion from tennis and that might get you to the point of ,"Ok I've got the sequence down, now I need to just clean up the disc golf form." Good luck.
