Is a thesis or dissertation required for completion of an LL.M. degree?

Yes, unlike almost all master's programs, an LLM degree does require to complete thesis or dissertation. Hardly any Law School is there which does not ask to complete a dissertation. A dissertation is considered a subject that is necessary to complete and secure good marks.

Even if you are seeking to move forward with PhD program, then also, ask you for a thesis-based master's program. as this will help the mentors to get to know about your research skills and other related skills.