Can I ask non-professors for a letter of recommendation?

This depends on the program that you are applying for. Generally, for professional programs like business and policy school, you should ask managers who can speak to your future leadership potential and ability to succeed in your chosen career path.

However, in other graduate programs, you should mostly ask your former professors or research supervisors to write your recommendation letters, unless you have worked in a job that corresponds closely with your chosen field (e.g., as a full-time research assistant).