I have had a very similar situation with a student who is also a lawyer! He is definitely more of a Level 3-4, but has chosen to start in our ESOL program from Level 1, so as to brush up on basics and fill in any gaps in his grammar and other skills. I had this student in a Level 1-2 conversation class last semester.
I understand your concern for the conversation class, especially with Level 1 students, who can often feel intimidated and/or shy about speaking already. I'm not sure how your tutoring/conversation classes are structured, but mine was a very casual setting, with the sole purpose of getting students to talk. Although the idea is to get the feel of natural, open conversation, there is definitely a need for moderation to keep the conversation appropriate, etc.
What I found worked best for me was to start the class by posting 3-4 discussion topics on the board - these could be in the form of questions ranging from "would you rather...?" to "what is your definition of success?" or - one that really got them talking and laughing - "Can men and women be just friends?" A great source with different discssion topics: http://iteslj.org/questions/
I also often incorporated YouTube videos that might spark discussion appropriate for their level.
Sometimes, I would post 3-4 questions on the same topic, and other times I would post 3-4 unrelated ones and ask the students to vote for the most interesting topic, and we would focus on that. The students get to talk about something interesting to them, but there's also some guidance so that everyone (including the more advanced student) has to keep it relevant to the topic. Even my Level 1 students were comfortable discussing topics such as corruption/politics in their own countries, as much as they could with their limited vocabulary. During our very first conversation meeting, I asked for general topics of interest to get a feel for the class's interests.
Hope some of this helps!