Professor Lucas Lepri demonstrates techniques for escaping a headlock and transitioning to mount. He begins by emphasizing the importance of balance and controlling either the opponent's arm or hips. He shows two options: putting a leg between the opponent's legs to create space and going to the side, or dropping both knees to take the opponent down. He then details how to prevent the opponent from reversing the position after the takedown. Lepri emphasizes using an underhook to control the opponent and then sliding a shin across the opponent's belly to secure mount. He also gives advice on countering attempts to bump or escape, stressing the importance of circling the foot and maintaining control.