"in a second lecture" is correct and can be used in written English.
You can use it when referring to a specific lecture (or presentation, class, etc.) that is the second one in a series or sequence. Example: "In a second lecture, the professor will discuss the various theories of evolution proposed by different scientists."
This attracted an overflow crows, and a loudspeaker was placed in a second lecture room, on a table.
In a second lecture with a second year applied mathematics class, Sandy was considering solutions of the logistic equation x m = qx m − 1(1 − x m − 1) for various values of the parameter q.
In a second lecture at the meeting, Reaven suggested that "the concept of insulin resistance is not as simple as the words themselves".
A second lecture, recorded in Berlin last year, presents a mordant picture of the present, through a reading of Victor Hugo's Les Misérables and the gameshow success of Susan Boyle.
In the second lecture, on Jan . 27 Mary T. Gotovich, a landscape designer, will discuss garden designs that blur the distinction between indoors and outdoors.
These students were enrolled in a first year level lecture course, Development, Structure, and Function of Organisms.
In the second lecture, his rich MCK alerted him to a potential error and aroused his natural desire to require the mathematics to be correct.
In her second lecture, Varda turned her attention to her more recent work making documentaries and art installations.
In the second lecture I spoke about these diverse manifestations of the Sharia in today's life.
Nineteen narratives were identified (of which four were classified as "stories"; see glossary) in the first lecture; eleven narratives (of which three were "stories") in the second lecture; and eighteen narratives (of which three were "stories") in the third lecture.
The first lecture was one hour in duration and the second lecture was for one and a half hours.
