The person who wrote biographies of Mazzini, Garibaldi, Shivaji, and Shri Krishna; stayed in America for some time; and was also elected to the Central Assembly was Lala Lajpat Rai.

Lala Lajpat Rai (1865-1928) was an Indian nationalist leader and freedom fighter who actively participated in the Indian independence movement. He was also known as "Punjab Kesari" (Lion of Punjab) and was a prominent member of the Indian National Congress.

Lala Lajpat Rai was well-educated and had a keen interest in writing. He wrote several books on Indian history, philosophy, and politics. Among his famous works are "The Story of My Deportation," "The United States of America: A Study," "Young India: An Interpretation and a History of the Nationalist Movement from Within," and biographies of Mazzini, Garibaldi, Shivaji, and Shri Krishna.

Lala Lajpat Rai went to the United States in 1914, where he delivered several speeches and lectures on Indian nationalism and freedom struggle. He also wrote extensively on the Indian freedom movement for American newspapers and magazines. His stay in the United States helped him to understand the American democratic system and its institutions, which he later incorporated into his own ideas for the Indian independence movement.

Lala Lajpat Rai was also elected to the Central Assembly in 1923. As a member of the assembly, he advocated for Indian independence and opposed British colonial policies. He also played a key role in the Non-Cooperation Movement of 1920-22 and the Civil Disobedience Movement of 1930.

In conclusion, the correct answer to the given question is Option 3: Lala Lajpat Rai, based on his works on the biographies of Mazzini, Garibaldi, Shivaji, and Shri Krishna, his stay in America, and his election to the Central Assembly.