Andrew Smith is a 3rd-degree BJJ black belt based out of Richmond, VA (Revolution BJJ). He runs BJJ Path, a video tutorial website.
Passing Leg Lasso Guard
"Leg lasso" can be one of the more intimidating types of guard to deal with, particularly when your partner takes a shallower hook with the lasso. It's possible for them to simply hold on and keep you in their guard, not allowing you to pass from the lasso itself (lest you get bicep slicer-ed or swept), and there is always the threat of the Omoplata and the triangle. Here is a breakdown of a simple game plan to get you started passing this dangerous type of guard. I'll also offer some adjustments you can do based on what your partner is likely to do as a counter.
Shallow Leg Lasso
Dealing with a shallow lasso hook is a bit different than dealing with a deep hook. A deep "leg lasso" implies that the person is shooting their leg straight through and up onto your back (for information on how to pass leg lasso guard, check out this previous tutorial). Fortunately, there's a very good, tried and true system in place for passing shallow leg lasso. Start by anchoring your right hand (assuming your right hand is caught in the lasso here) as low on your partner's lapel as possible (a belt will also work). Your left hand should already have inside control on the pants, as described previously. Next up, while balancing on your toes, pivot your right knee in (if you practice Muay Thai, it's just like throwing a curve knee in Thai Boxing) right at your partner's toes, effectively working to peel the lasso hook free of your arm. A word of caution: make sure not to "peel" at your partner's heel here, or else you'll end up inadvertently heel hooking your partner! Next, make a circle with your right arm, and duck your head under your partner's leg, ending up back in the middle (and making a sort of shield with your right forearm). Finally, finish what essentially amounts to an X-pass here.
Dealing With the Transition to De La Riva Guard
Here's an important conceptual tip: make sure to control the non-lasso leg before moving on to the lasso hook, at least with as much control as you can muster. Otherwise, your base is going to be all kinds of terrible. This is particularly viable as your partner attempts to make a transition to De La Riva guard once you drive your right knee forward. If they're stepping on the inside of your left knee with the non-lasso hook, it's going to be rough for you. As they make the switch to De La Riva, make sure you're keeping constant pressure on their right leg (with the aforementioned inside control), and then step out against the DLR hook with your left leg, coming forward with a very wide base. From here, it makes the most sense to either use a right forearm shield (as shown in the top video), or else to transition into a nice knee cut pass as shown in the bottom video.
An Alternate Path
After peeling the lasso hook, as an alternative, you can try passing to the side of the lasso itself. Be sure to duck your head under, as before, but this time, follow to the same side with your body, as shown in the video. Be aware, however, that a basic guard maintenance movement is going to be wide open for your partner as you duck to the right, so you're going to need to follow up with a leg drag or double underpass sequence (or a more advanced back take off of your partner's reaction).
Practice Makes Perfect
The leg lasso is really just like any other type of guard: once you understand the basic mechanics, it's much easier to shut down. These passes certainly work well in conjunction with the aforementioned knee cut pass and the leg drag, and there are other far more basic options you'll want to be prepared to use in combination. As always, have fun, and don't be afraid to experiment when trying out these new positions (and don't be afraid to be swept or submitted, especially if you learn something in the process!). Let me know how these work for you, too.