Final answer:
Igor Stravinsky is the correct answer, as he toured giving concerts and lectures until his death in 1961. Albert Einstein, while a prominent figure in the US, was not known for giving concerts but for his scientific work and political advocacy until his death in 1955.
Step-by-step explanation:
The person who became a US citizen and toured giving concerts and lectures until his death in 1961 was Igor Stravinsky. Though Albert Einstein became a highly recognized figure in the United States, he did not tour giving concerts; he was a theoretical physicist who engaged in writing, lecturing, and advocating for various intellectual and political causes until his death in 1955. Martin Luther King Jr. and Nikola Tesla both made significant contributions to society but do not fit the description provided in the question.
It was Igor Stravinsky who fits the description as after settling in the US, he continued to shape the course of music through his compositions and influence until passing away in 1961. Einstein, though a famous refugee from Nazi Germany and an active cultural figure, was not known for musical tours but rather for his work in physics, including his involvement in sending a letter to President Roosevelt in 1939 about the dangers of atomic weapons development by Germany.