A "protected tree" in Los Angeles is any of the following Southern California native tree species which measures 4 inches or more in cumulative diameter, 4 1/2 feet above the ground level at the base of the tree (DBH):

(a) Oak tree including Valley Oak (Quercus lobata) and California Live Oak (Quercus agrifolía), or any other tree of the oak genus indigenous to California but excluding the Scrub Oak (Quercus dumosa).
(b) Southern California Black Walnut (Juglans californica var. californica)
(c) Western Sycamore (Platanus racemosa)
(d) California Bay ( Umbellularia californica)

This definition shall not include any tree grown or held for sale by a licensed nursery, or trees planted or grown as a part of a tree-planting program.

No person shall relocate or remove any protected tree, without first having applied for and obtained a permit from the Board of Public Works, Urban Forest Division. See the full ordinance text here.

If you observe a protected tree(s) being cut down, please take pictures and contact the City of LA's Bureau of Street Services (StreetsLA), Urban Forestry Division at  (800) 996-2489 and email Tim Tyson (Chief Urban Forester) at Tim.Tyson@lacity.org right away.  For more information, see https://streetsla.lacity.org/urban-forestry-division.

There is also a proposal from January 2017 to add the Toyon (Heteromeles arbutifolia) and the Mexican Elderberry (Sambucus Mexicana) species to the Protected Tree Ordinance, but it has not been passed by the City Planning Commission.
 

The Mexican Elderberry and Toyon have been proposed to be classified as protected trees because they are native species, promote native wildlife and habitats, can grow to a variety of sizes, and are species that are important to the history and identity of Los Angeles. The Mexican Elderberry and Toyon are native to California and require very little water. Both species produce berries, attract butterflies, birds, and other wildlife, and are important to maintaining natural habitats. When one of these trees is removed, the impacts go far beyond aesthetics and affect entire ecosystems. Additionally, the Toyon tree is said to have inspired the name for Hollywood and is the official City Native Plant.

Your neighborhood council can submit a community impact statement (CIS) to Council File 13-1339.