A more idiomatic translation might be “please get this done”; the “needful” phrase might also be a signal that the writer isn’t that familiar with idioms used in other English-speaking countries.
Hobson-Jobson[1] had a great early compilation of some phrases that arose in the subcontinent— many are still in use.
[1] https://en.wikipedia.org/wiki/Hobson-Jobson
PS. there’s some evidence from Google Books[2] that “do the needful” might be an old English legal term as well. More research is definitely required. The bigger point is, the phrase’s popularity in India may be because it mirrors a Sanskrit-derived word often still used in Indian legal contexts.
[2] A Glossary of Words and Phrases Usually Regarded as Peculiar to the United States, 1860
https://books.google.com/books?id=VXdIAQAAMAAJ&pg=PA428&dq=%...