Follow Jacob up until you are separated.
When chaos around starts and boulders start falling from everywhere, do not look back - sprint through the corridor and pass by the blocked passages.
Lara should reach a largish room, where there are three opponents. Try to eliminate them silently, e.g. with a poison arrow.
Approach the lift's control panel and use it. The lift will come down a bit, but it will get stuck.
Cross the room and push the cart under the ramp. Jump into the cart and climb onto the ramp.
Lara will find a knife that you will be using for both cutting ropes and elimination of unaware enemies.
Cut the first rope next to the table with the knife on. Thanks to this, Lara will be able to jump over to the other side of the ramp, near the lift.
Approach the lift and cut through both cables there. The lift will fall down.
Jump off the ramp, to the ground level and walk onto the lift. From there, jump onto the ice wall on the right, climb higher and jump back towards the shaft. Walk around it on the left and climb higher.