The lion-tailed macaque, a species of primate, is naturally found in the Western Ghats of Kerala. This mountainous region, located in the southern part of India, is known for its rich biodiversity. The lion-tailed macaque is specifically found in the dense forests of the Western Ghats, which provide the necessary habitat for their survival.

Option 1, Eastern Ghats of Andhra Pradesh, is incorrect. Although the Eastern Ghats are another mountain range in India, the lion-tailed macaque is not naturally found there.

Option 3, Shivalik Hills of Northern India, is also incorrect. While the Shivalik Hills are a part of the Himalayan foothills in Northern India, they are not the natural habitat of the lion-tailed macaque.

Option 4, Hills of North-East India, is also incorrect. While North-East India is known for its diverse wildlife, the lion-tailed macaque is not naturally found in this region.

Therefore, the correct answer is option 2, Western Ghats of Kerala, as this is the natural habitat of the lion-tailed macaque.