Lecturing.
The past participle of the verb "lecture" is "lectured."
"Since she knew what the lecture was about" in the first sentence is replaced by the participle phrase "Knowing what the lecture was about" in the second sentence."Knowing" is the present participle of the verb "to know". Here it works like an adjective describing "she". She was a "knowing" woman. She was a "knowing-what-the-lecture-was-about" kind of woman.
Getting is the present participle of get.
The present participle is doing.
Being is the present participle. The past participle is been.
Presenting is the present participle of present.
Presenting is the present participle of present.
The present participle is choosing.
The present participle is walking.
The present participle is cleaning.
The present participle is shaking.
The present participle is coming.