Go to a search engine and do a basic search. Experiment typing in different search queries into the search bar. Terms such as "law school," "no fee," "no application fee," and "no application fee law school" will provide some information.
Create a list of potential schools of interest and do things the old-fashioned way by calling the admissions office of these schools. When calling, ask the school representative if the school has an application fee or not.
Inquire with schools that have an application fee if there is an exemption available for fees. For example, some law schools offer incentive for potential students if they apply early. A school may waive a fee if said student applies on or before a certain date.
Contact the Law School Admission Council at (215) 968-1001 and inquire with representative regarding known schools that require no fee to apply.
Speak with a law school advisor about this issue. If you don't have a law school advisor, contact your undergraduate school and refer with representative regarding securing a counselor. Most undergraduate colleges offer this services to alumni.