Lara will lose the entire equipment after the first stage of Cozumel and the cut-scene with the airplane crashing in the Peruvian Jungle. Below, you can find the guide to finding the three most important pieces of equipment - the knife, the bow, and the climbing axe.
Getting back the knife
You can get the knife back after completing the first stage of the jungle and reaching the main hub of that location - the first camp. We're talking about the place, where the lake with the first part of the airplane wreckage is located.
Approach the yellow propeller and examine it. You will have to dive. Reach the fragment of the plane from the picture above. Lara will hence obtain the knife. You will have to use it right away to kill an aggressive eel.
Getting back the bow
Get back to the Surface and use the knife to try and cut the rope shown above. You will learn that the knife isn't sharp enough.
You have to find any 3 Salvage crates - you can try and reach those indicated on the map or find some yourself. After getting enough materials, go back to the camp in the jungle. Go to the inventory tab and spend the resources on creating a Makeshift Knife. This will let you cut the rope.
Cutting the first rope won't do the trick - there's another one that needs cutting. In order to reach it, you have to climb the "interactive" tree and jump onto the rock ledge above. The place where you can cut the rope is shown above.
Now you can reach the place, where the cargo was dropped. The Recurve Bow is in the oblong crate shown above.
Getting back the climbing axe
Reaching the climbing axe requires you to get further down into the jungle, which used to be unavailable before you'd gotten the bow. Explore the western part of the first stage of the jungle. In the place shown above, Lara has to use a rope arrow to unwind the rope. This will let her get to the other side.
On your way to the other part of the wreckage, Lara will encounter, among others, some jaguars - tips on fighting them can be found in our walkthrough of the game. The location of the wreckage is shown in the picture above.
You have to walk the fallen tree and complete a short slide down. A cut-scene will commence, showing her meeting Johan - the Climbing Axe will be automatically added to the inventory.