I will enlist down some of the top universities for BBA or BMS in Lucknow -

1. University of Lucknow
2. Bhalchandra Institute of Education and Management
3. Institute of Co-Operative and Corporate Management Research and Training
4. Integral University
5. Amity University
6. National university Lucknow
7. Shri Sharda Group of Institutions

Refer to the site below for more detailed information about the same -

https://bschool.careers360.com/colleges/list-of-bms-colleges-in-lucknow

https://bschool.careers360.com/colleges/list-of-bba-colleges-in-lucknow

Best wishes. Thank you.