Option 1: Abul Fazl was a prominent scholar and advisor in Akbar`s court. However, there is no evidence or historical records to suggest that he translated Bhaskaracharya`s Lilavati into Persian. Therefore, option 1 is not the correct answer.
Option 2: Faizi was a renowned poet and scholar who served in Akbar`s court. He was known for his expertise in Persian language and poetry. It is mentioned in historical records that Faizi translated Bhaskaracharya`s Lilavati into Persian. Therefore, option 2 is the correct answer.
Option 3: Fathullah Shirazi was an astronomer and mathematician in Akbar`s court. While he made significant contributions to the fields of mathematics and astronomy, there is no evidence to suggest that he translated Bhaskaracharya`s Lilavati into Persian.
Option 4: Ataullah Rashidi is not a identified scholar in the context of Akbar`s court. Therefore, option 4 is not the correct answer.
In conclusion, the correct answer is option 2, Faizi. He was the scholar in Akbar`s court who translated Bhaskaracharya`s Lilavati into Persian.