how would you encourage a leluctant peer reviewer.

I would ask a question first

That's a good idea, but what kind of question(s) would you ask? Depending on what they are reviewing, there are many different questions that could be asked. Here are some possibilities.

What aspects seemed especially good about the paper?

Were there any parts that you had to reread to understand what I was saying? Were there any parts that you could not understand?

Were my arguments and evidence effective? Did I miss any potential points?

Would my paper be effective in convincing you? Why or why not?

I hope this helps. Thanks for asking.