Technically no. The GAO bid protest rules do not require a GAO protest to be filed by a lawyer. However, you should strongly consider using an experienced bid protest attorney.
GAO protests have aggressive timelines and can be a complex technical process. Because GAO timelines are driven by regulation, there is no room for error, if you miss a deadline, GAO will dismiss the protest.
In addition, only an outside attorney can review the full agency file. A GAO Protest has a protective order that allows those admitted to it full access to the procurement file. As this file has competitive information for all of the bidders, only an outside attorney can be admitted to the protective order. Most protests are won based on the information in the procurement file.