There are a number of ways to reach this cave from the entrance to the Hushed River Valley.
Via Pensive Vista
One method is to head eastwards from Stairsteps Lake to Many Falls Vista and climb down towards Twin Sisters Falls. From there, head northwards towards Valley Cave, and turn right at the cliff-face. Climbing two ropes will allow the player to reach Pensive Vista, from which Lake Cave is a short stroll northwards. This method is good if one wishes to explore the eastern part of the region and search Moose Overlook for a possible bow and the Landslide for a possible Hidden Cache, but requires three rope climbs, and is nearly impossible to complete in one day.
Via Offset Falls
Another way to get to Lake Cave is to head due northward from Cloudtop Falls and pass right below the foot of Offset Falls. Heading north and then northeast from there will lead the player past a small frozen pond and one of the entrances to the Ice caves to a climbing rope. Heading eastwards will lead past Mammoth Falls and Quarreling Falls and straight towards Lake Cave. This is a very direct and easy to navigate route, but players will have to be mindful of wolves and possibly a bear.
Via the ice caves
The final way to get here is to head northwards from Stairsteps Lake towards the Hushed River and enter the ice cave located next to Reclusive Falls. From there, the player will have to navigate the cave until they reach a room with a climbing rope. After the climb, leave the cave and turn left. From there a walk eastwards will lead to Monolith Lake and Lake Cave. While this method is the safest from predators and weather, there is a risk of getting lost in the ice caves if one doesn't bring a light source.
A frozen corpse may spawn here, along with a backpack and campfire. Various items of food and drink are sometimes found here too, along with a possible research book. Rifle and revolver ammunition spawn here on occasion too. Sometimes, a revolver may be found here.
This cave can be very useful for hunting the moose that spawns nearby on Monolith Lake, as it is too small for the moose to fit into. The cave can also be used in order to cure hides, as it is considered to be a sheltered cave.
Because predators don't spawn near the cave and there's lots of rabbits to snare nearby on the east end of Monolith Lake, some players may find that it makes for a decent safehouse. This is especially true if one has killed the moose on the lake. One disadvantage of this cave is that it's very noisy, due to the waterfall nearby. If the sound bothers the player, Pensive Vista may be a quieter option.