The first mission in what is today the greater Los Angeles area was San Gabriel Arcangel, founded on September 8, 1771. The church in Los Angeles (the official name was Iglesia de Nuestra Senora de Los Angeles) was founded in1784 as an asistencia (or sub-mission) to Mission San Gabriel. The site chosen was at the first Spanish pueblo of Los Angeles, founded by Governor Don Felipe de Neve on September 4, 1781. There was originally a small chapel on the spot.
A more elaborate church was constructed between 1814-1822. Many of the area missions donated supplies to the new church. San Gabriel, for example donated two barrels of brandy, a bultro of San Vincente Ferrer and two bells, which are still in use today. The Old Plaza Church has gone through extensive remodeling and expansions over the years, most recently in 1965 when the church suffered extensive earthquake damage.
So the answer to your question is that this church was a sub-mission originally erected during the mission era. I would think your son could do a wonderful project on this important structure but you will have to check with his teacher to see if this would be permitted, or whether they want the students to focus on one of the 21 primary missions.