Introduction:
The Chinese Buddhist pilgrims mentioned in the options were renowned travelers who embarked on journeys to India to study Buddhism and collect Buddhist scriptures. While three of them, Fa Xian, Xuan Zang, and I-Qing, undertook pilgrimages to India, Lao Tzu was not associated with Buddhism nor did he visit India.

Explanation:

Fa Xian:
- Fa Xian, also known as Faxian or Fa-hsien, was a Chinese Buddhist monk who traveled to India between 399 and 414 CE.
- He embarked on his journey to India to collect Buddhist scriptures and study Buddhism at its source.
- Fa Xian spent several years in India, visiting significant Buddhist sites such as Bodh Gaya, Sarnath, and Nalanda.
- He returned to China with a vast collection of Buddhist scriptures, which he translated into Chinese.

Xuan Zang:
- Xuan Zang, also known as Hsuan Tsang or Tripitaka, was another prominent Chinese Buddhist monk and scholar.
- He embarked on his pilgrimage to India in 629 CE and returned to China in 645 CE.
- Xuan Zang's journey to India was primarily motivated by his desire to study Buddhist philosophy and collect Buddhist scriptures.
- He traveled extensively across India, visiting numerous monasteries, universities, and sacred sites.
- Xuan Zang's journey is well-documented in his travelogue, "Records of the Western World," which provides valuable insights into the cultural, religious, and political aspects of India during that period.

I-Qing:
- I-Qing, also known as Yijing or I-Tsing, was a Chinese Buddhist monk who traveled to India in search of Buddhist scriptures.
- He embarked on his pilgrimage to India in 671 CE and returned to China in 695 CE.
- I-Qing spent over a decade in India, studying Buddhism and collecting scriptures.
- He visited various Buddhist centers, including Nalanda, where he received teachings from eminent Buddhist scholars.
- I-Qing's travelogue, "A Record of Buddhist Practices Sent Home from the Southern Sea," provides valuable information about the Buddhist institutions and practices he encountered in India.

Lao Tzu:
- Lao Tzu, also known as Laozi, was an ancient Chinese philosopher and the founder of Taoism.
- While he was a significant figure in Chinese philosophy, Lao Tzu was not associated with Buddhism.
- There are no historical records or accounts that suggest Lao Tzu visited India or had any connection to Indian Buddhism.

Conclusion:
In conclusion, among the Chinese Buddhist pilgrims mentioned in the options, Lao Tzu was the one who never visited India. Fa Xian, Xuan Zang, and I-Qing were renowned travelers who undertook pilgrimages to India to study Buddhism and collect Buddhist scriptures.