LAMP's structure and priorities are governed and determined by its members, and its Bylaws are contained in the LAMP Prospectus, which can be revised by a vote of the representatives at LAMP member institutions. The members of LAMP also elect the LAMP Executive Committee, which sets and acts on organizational priorities.

LAMP is made possible through the support of the Center for Research Libraries, which serves as its administrative, fiscal, and legal agent.

LAMP meets once a year, at the conference of the Seminar on the Acquisition of Latin American Library Materials (SALALM), at which time LAMP considers and votes on funding proposals for acquisitions and new projects.  Institutions or nonprofit organizations that maintain a library and whose interests coincide with LAMP are welcome to Join LAMP.

LAMP was founded as the Latin American Microform Project in 1975 by members of SALALM. In 2015, LAMP updated its name to stand for 'Latin American Materials Project', in recognition that its projects may include digitization as well as microfilming. An article about LAMP's History describes the work of LAMP over the years.