LAPL
Starting in the middle... here is the school built on the corner the northeast corner of Hollywood Boulevard and N. New
Hampshire in 1915...at a time when what was carved over the door would have been a teachable moment if not already
understood by the pupils within (whatever happened to "pupils"?).
Before the MCMXV building, however, there was this incarnation of the Los Feliz School:
The Bruce Torrence Hollywood Photograph Collection (obvs)
Note that short, apparently concrete, fence along Hollywood Blvd in both shots above. It's still
there, if without the swag of chains:

Google
The MCMXV school is gone--I didn't do a whole lot of research as to what happened to it, but perhaps it suffered irreparable damage from the 1933 Long Beach earthquake. Many SoCal schools did (i.e., Thomas Jefferson HS), and they were replaced with contemporary architecture. Anyway, if the MCMXV building wasn't torn down in the '30s, it was removed from the site at some point after a new Los Feliz School went up, set back on the lot from Hollywood Blvd, facing New Hampshire:

Google
Back to the boulevard for a minute... I'm sure you noticed the fenced-off subway entrance on
the corner. Here's the other end across the street:

Google
That's Barnsdall Park to the right. These were the views from there:
The Bruce Torrence Hollywood Photograph Collection
USCDL
One last shot...the earlier school coming down for the MCMXV edition:
The Bruce Torrence Hollywood Photograph Collection
It looks like a second story was added somewhere along the line...