LAPP began in 1954 when a group of mothers formed a high quality co-operative preschool to serve the growing community. The parents wished to share responsibility for the administration, maintenance, and working program of the school. They formed LAPP as a non-profit corporation to furnish housing, equipment, supplies, and part of the Teacher/Directors' salaries.

The Mountain View-Los Altos Union High School District (School District) agreed to supervise the program and share payment for staff salaries. As part of the School District's Adult Education Department, the preschool became the laboratory for a parent education class. The Los Altos United Methodist Church granted the use of their facilities.

In 1998, the School Board leased land to LAPP at the west end of Los Altos High School. Through major fund-raising efforts and community and member donations, the preschool purchased a portable classroom module and furnished the play yard.

In the summer of 2011, the membership and alumni of LAPP moved the school to its new home at the Covington Elementary School campus, beginning a new partnership with the Los Altos School District. LAPP remains a part of the Mountain View-Los Altos High School District's Adult Education Program. California Adult Education standards and the co-operative preschool philosophy require LAPP parents to serve as active members and staff assistants. In 2014, LAPP celebrated sixty years in the Los Altos community with a series of events for members, alumni and the general public.