A webcam is not required for the use of Respondus Lockdown Browser. Respondus offers an additional product called Respondus Monitor which requires a webcam (for remote video proctoring). But most instructors do not require Lockdown Browser + Monitor.
If an instructor does intend to require Respondus Monitor for the exam, ensure that the Monitor setting is enabled for the quiz. ("Required" should show up in the Monitor column of the LockDown Browser Dashboard) AND the exam's title must end with:"- Requires Respondus LockDown Browser + Webcam" (this exact string).
If Respondus Monitor is not meant to be enabled for the quiz, make sure that the word "webcam" does not appear anywhere in the quiz title.
For more information: https://support.respondus.com/hc/en-us/articles/4409604349595-Exam-title-states-a-webcam-must-be-used-but-the-exam-settings-don-t-indicate-its-selected