The question is about identifying the veteran filmmaker who received the Padmapani Lifetime Achievement Award for Indian cinema in January 2025. Let's analyze each option to determine the correct answer:

1. Sai Paranjpye: Sai Paranjpye is a renowned Indian filmmaker known for her contribution to Indian cinema with films like "Sparsh," "Chashme Buddoor," and "Katha." Her extensive work and impact on the industry make her a deserving recipient of lifetime achievement awards.
2. Shyam Benegal: Shyam Benegal is another influential filmmaker in Indian cinema, known for his parallel cinema contributions. While he has received numerous awards, he is not mentioned as the recipient of the Padmapani Lifetime Achievement Award in January 2025.
3. Vishal Bhardwaj: Vishal Bhardwaj is a contemporary filmmaker and composer known for movies like "Omkara" and "Haider." Although a significant figure, he was not awarded the Padmapani Lifetime Achievement Award in January 2025.
4. Mira Nair: Mira Nair is an internationally acclaimed filmmaker known for "Monsoon Wedding" and "The Namesake." Although she has received numerous accolades, she was not the recipient of the mentioned award in January 2025.

Based on the options and the context provided, Sai Paranjpye received the Padmapani Lifetime Achievement Award for Indian cinema in January 2025.

Conclusion: The correct answer is Sai Paranjpye, who was recognized for her significant contributions to Indian cinema over the years.