The Lost Domain - Sprinting Jump Upgrade
As Lara slides into the level, your notebook is updated (55/62): "Find Eckhardt's old lab. We need that third Periapt Shard." (Again, this page on Von Croy's Notebook lists all entries.) The "Took Care" achievement/trophy for beating Boaz also unlocks here.
Just ahead, the passage splits. Go to the right.
Soon you'll come to a slope above a lava pit. You can't get the large health pack behind the bars yet.
Slide down the slope and jump just before the end to land on the nearest stone pillar. (You can steer Lara in the air a little bit, but don't oversteer or she'll veer off into the pit.)
Walk to the far edge of the last stone in this cluster. Then take a short hop (Walk + Jump) to the freestanding pillar ahead.
Again, walk to the far edge, then take a regular standing jump to the ledge with the lever.
As Tomb Raider Logic™ would have it, completing this sequence gives Lara a lower-body strength upgrade. She also gains the ability to do a special sprinting jump, which will be very useful shortly.
Pull the lever to raise the gate back at the cave entrance.
Climb onto the wooden walkway...
...and return along the edge of the pit to the tunnel.
Pick up that large health pack (1), exit through the open gate, and go to the left to get back to the main tunnel.
Turn right at the intersection and continue to another cavern. This one has a lever near the entrance.
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