An Honorary District, Not an HPOZ
Silver Lake has no City Historic Preservation Overlay Zone. What it has is the National Register-listed Silver Lake Residential Historic District, recognizing a notable concentration of mid-century modern and Period Revival architecture, with work by Gregory Ain, Craig Ellwood, John Lautner and Rudolph Schindler represented, plus the smaller Childs Heights Residential Historic District nearby. Both are honorary federal listings, not HPOZ-style overlays, so they don't carry the roof-material design review that a genuine HPOZ, like Echo Park's Angelino Heights next door, requires. The Silver Lake and Ivanhoe reservoirs themselves are a separate individual site designation, not an area-wide overlay.
In practice, that means a Silver Lake reroof needs the standard LADBS permit but not a historic-district design review, even on an architecturally significant house.