Famous people sometimes give lectures/speeches/talks to public groups (often after their fame has begun to fade). One meaning of circuit is a journey (usually a big loop or circle). He made the New York, Chicago, San Francisco, Los Angeles. The "lecture circuit" is to give speeches (lectures) to groups, often for large amounts of money (sometimes $25,000 for one speech).

"Took to" can mean "began a habit" or "started a new pattern in life." Thus, "he dressed informally when he was just an assistant, but took to wearing a suit when he became a vice-president." Or, "Theodore Roosevelt had been a sickly youth, but as a young man he took to engaging in strenuous outdoor activity." Before the days of radio and television, entertainment consisted of live performances in theaters. Often these were presented by touring companies who traveled from town to town. Often they were managed by entrepreneurs who operated a chain of theaters. The bookings would be arranged so that performers traveled in a closed loop or "circuit." The Keith Circuit, for example, was a vaudeville circuit. In the United States, certain kinds of judges also traveled, hence the term "circuit court." Certain religious denominations, notably Methodists, had itinerant preachers who traveled a "circuit." Lectures were actually a common form of entertainment or education in the United States in the late 1800s, and, like vaudeville entertainment, were organized in circuits. "The lecture circuit" means that a lecturer earned money by signing up with an agency, who would book them into halls, and they would travel from town to town giving lectures. So, "Hopkins took to the lecture circuit" means that he started to make a career of giving public lectures for pay. Nowadays we would be more likely to say "In his later years, so-and-so took to accepting well-paid speaking engagements."