The correct answer is option 4, Nilgiris. The Lion-tailed macaque is a species of monkey that is naturally found in the Nilgiri Biosphere Reserve, which is located in the Western Ghats of India.

Option 1, Shivaliks, is incorrect because the Shivaliks is a range of hills located at the southern foot of the Himalayas, and it is not the natural habitat of the Lion-tailed macaque.

Option 2, Pachmarhi, is incorrect because Pachmarhi is a hill station located in Madhya Pradesh, India, and it is not the natural habitat of the Lion-tailed macaque.

Option 3, Annamalai Sanctuary, is incorrect because Annamalai Sanctuary is a protected area in Tamil Nadu, India, and although it is a part of the Western Ghats, it is not specifically known as the natural habitat of the Lion-tailed macaque.

Therefore, the correct option is option 4, Nilgiris, as the Lion-tailed macaque is naturally found in the Nilgiri Biosphere Reserve in the Western Ghats.