A bunch of things come to mind because there are a lot of variables. Arm in guillotine? No arm? Is he falling to his back? Is he pressuring forward? I'm going on the assumption that you've already whipped up and you're on your side with an arm underhooking a leg.
First thing that comes to mind is that he rolls to his back to finish the guilli. If he does, simply hold the lockdown, let him roll to his back, block the near hip and pass to side control. If he holds the guilli just hit him with the von flue.
If you have his foot and he guillotines, just power through old school and get to side control.
If it's an arm in guillotine, use the arm that's around his waist to reach up and grab his trapezius muscle. Stretch the LD while straightening your back and neck and pushing the arm off your head.
There's an armdrag available if you prevent his hands from clasping and you get wrist control.
And remember to always whip that leg around and make him base out with his hands or force him to sprawl. If he bases out, you're safe because his hands are occupied. If he sprawls you always have dogfight.
Speaking of dogfight. In my opinion, all LD players should really get good at it. All half guard players in general for that matter. I've been seeing a lot of high level guys using this strategy for LD. If they can't get under you for sweeps, they'll get up to dogfight and take it from there. If you get good at dogfight, you have a lot more options.
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