Sri Lanka was a separate crown colony from the British Raj since the end of the 18th century. Sri Lanka and Burma became seperately independent from India because they had become separate colonies.

A followup question is why Sri Lanka mattered geopolitically. Wikipedia has one sentence:

Its geographic location and deep harbours made it of great strategic importance from the time of the ancient Silk Road[9] through to World War II

If it was access to India, then surely accessing India would be easier than an island offshore. The economy and goods didn't seem to stand out, again with India right next door and having the same exports.

Since you didnt specify, and /u/sh0rug0ru already gave a good account for the why post-colonialisation, Ill account for pre-independence.

The island of Lanka was part of Maurya Empire which spanned a better part of the sub-continent. Following the Mauryan dynasty, you have the Pandyan and Chola dynasties which also occupied large parts of the island.

There was also a lot of intermarriage and assimilation between the kingdoms present in Lanka and India as well. In fact, the last dynasty of Lanka- the Nayaks- were related to the south Indian Nayaks.

So, the island of Lanka was part of Indian kingdoms at certain points in its history. However, the Democratic Socialist Republic of Sri Lanka was never a part of India.