I never got in such a situation, but I've cleared about ten such lairs and think that you need one correctly placed High Explosive. Move the map and see which direction has the most of unexplored area. Place the explosives right near the door that can't be passed through.
You can play this mission separately from you campaign via Mission Generator. Start the game, press New Battle in main menu, choose the mission Cyberweb Lair. After exploration you might see which 10x10 map blocks the map consist of and might recognize the ones that you see in your campaign.