When discussing southpaw vs orthodox matchups, fight fans and analysts tend to grossly oversimplify the matter. The advice you always hear is that the lead foot must be kept on the outside to line up the rear hand. This—along with the closely related notion that jabbing isn’t important—is false. Stepping the lead foot outside to land the rear hand is merely ONE aspect of southpaw vs orthodox strategy. In fact, it can even be disadvantageous to do so.
Take McGregor's last win before getting signed by the UFC. His opponent takes a big step outside, which theoretically gives him the advantage. However, the step is easily seen by McGregor, who slips it and starches Buchinger with a perfect counter. You see, the step not only telegraphs the punch but also leaves the aggressor in a very bad position should he miss. The feet are left square with the head forward, meaning McGregor's counter lands clean and he ends up in perfect position to continue his attack if Buchinger doesn't go down. Just like in orthodox vs orthodox fights, fighters can attack angles towards the centerline (inside) or toward the back (outside) of their opponent. By getting too committed to chasing one, you can expose the other. Now of course a huge mistake is that Buchinger had no set up. McGregor was controlling his lead hand, so the right straight was the most predictable attack and easily dealt with. The trick here is that to most effectively use the lead hand for set ups, a fighter must find a way to make their lead hand a threat.
This is where things tend to get really messed up. The general assumption is that both the orthodox fighter and the southpaw fighter will be handfighting with their leads, effectively neutralizing each other’s jabs (and in many cases every strike from the lead side). This is a dirty, dirty lie that I can only assume is being secretly perpetuated by southpaw’s to make their lives easier. If someone is able to negate your jab just by playing patty cake with it, that simply means you lack the versatility to do anything about it. There are many solutions to this and quite honestly they aren’t much different from what you would do if an orthodox fighter was sticking his hand out to smother your jab. You can step inside his lead foot to jab, you can jab to the body, you can hook over his extended arm (from inside or outside), you can hook to the body under his extended elbow (southpaws stand liver forward!) or you can even slip outside the arm and throw a left uppercut through his armpit--my personal favorite:
You can also occupy his lead hand and switch kick his right side or really use any number of attacks. The jab still works against a southpaw as long as you are versatile enough to not let your opponent take it away from you. And once you have your opponent sensitive to you stepping inside to land it, you can start stepping outside with it to line up the rear hand in "textbook" fashion:
And it's a shame to use the lead only for set ups. The lead hand can be incredibly dangerous in orthodox vs southpaw matchups, both for attacking and for countering.
Other good examples of fights that show conventional wisdom being broken include Johnson vs Lauzon, Machida vs Silva, Machida vs Rashad, Diaz vs Maynard 2, Belfort vs Bisping, Pettis vs Lauzon. For the boxing fans, Lara loves to land his left straight from the inside foot position and hit Canelo with a few good ones while moving that way just a few days ago, and Cotto expertly used his jab to set up his hook while stepping inside against Martinez recently as well.
This post isn't meant to be a technical analysis like most of my articles and it definitely isn't meant to be a how to guide on fighting a southpaw--because that is exactly as problematic as it would be trying to write a guide on how to fight an orthodox opponent as if they're all the same. This thread is just to get the discussion on a deeper level and open people's minds to the many different options available to a fighter that often get neglected.
tl:dr: Drown 'em at birth!
But seriously, all southpaws aren't the same fighter and there is no simple rule to fighting one. The best southpaws can attack angles on either side and hurt you with either hand. You can do the same back to them. The jab still fucking works and you CAN circle towards their power hand if you know what you're doing.