Chapter 3: Freeman Pontifex 2
When both antlion guards are defeated, follow Vort to a generator that powers a lift. The lift is stuck overhead, so for now look for a ladder to the left of the lift and climb it. Once on top of the structure surrounding the base of the lift, look along the rock wall for a narrow path that leads up. As you go up the path, watch for a black headcrab that jumps out from behind a boulder you move from your path.
The hillside path lets you overlook the next level of the structure built around the lift. Move carefully across the beams (the boards laid lazily across the beams will fall) to overlook the top of the elevator enclosure. Use the Gravity Gun to open up the shaft on top of the elevator enclosure so you can jump in. Dislodge the pick axe from the elevator's lever to drop the lift down to ground level.
Allow your companions to enter the elevator with you before pressing the switch inside the enclosure to raise the lift. Ride the lift to the top of the cliff where you'll find an entrance to a tunnel within the cliff.