Which of the following awards was won by Lata Mangeshkar in the year 2001?

The correct answer is Bharat Ratna.

Let us look at the details of the awards received by Lata Mangeshkar:
1. Bharat Ratna: This is India's highest civilian honor. Lata Mangeshkar was awarded the Bharat Ratna in the year 2001 for her extraordinary contribution to music and arts in India.
2. Padma Vibhushan: She received India's second-highest civilian award in the year 1999.
3. Dadasaheb Phalke Award: She received this prestigious award for outstanding contribution to the growth and development of Indian cinema in the year 1989.
4. Filmfare Lifetime Achievement Award: She received this award in the year 1993.

Therefore, the award won by Lata Mangeshkar in the year 2001 is the Bharat Ratna.