If you are flattened out on your back with double unders, try swinging one arm fast towards do your opponent's armpit (this does not require precision, that's just the general direction) while bring your knees towards your chest (the lockdown will still be in, you are taking them off their balance point). You are trying to push them off your chest so you can roll to your hip. That's a variation of the Whip Up.
Also, try chin strapping anyone trying a Buttock Compressor. They are trying to back out of your lockdown - it's hard to move backwards when doing so drives someone's hand into your throat. Sometimes people can still manage to break open the lock down, but that's when you let go and push their head down while scooting backwards and out. I often end up in butterfly guard when I do that.
Also, try chin strapping anyone trying a Buttock Compressor. They are trying to back out of your lockdown - it's hard to move backwards when doing so drives someone's hand into your throat. Sometimes people can still manage to break open the lock down, but that's when you let go and push their head down while scooting backwards and out. I often end up in butterfly guard when I do that.