Lafayette Park occupies a steeply sloped site at Gough/Sacramento/Laguna/Washington. The post-quake fires on earthquake day (4/18/1906) were far away, but early on day 2 (4/19/1906) fire from Chinatown crested Nob Hill and rapidly spread west through Polk Gulch, while at the same time fire from near City Hall proceeded north along Van Ness. Faced with a tenuous water supply, firemen fought to keep the fire from spreading further west by dynamiting large homes on the east side of Van Ness to create a fire break. The fire crossed to the west side of Van Ness at Sutter and burned west to Franklin and then north, but firefighters stopped its western advance at Franklin/Clay (a block from Lafayette Park) at around 3 AM on day 3 (4/20/1906).
Kennedy's fire timeline describes the progress of the fire in detail. 1905 Sanborn (V. 3 sheet 260) shows details of the area before the fire. Punnett's Two Years After map shows the burned area.
These postcards all show the same view; a higher resolution image is here. Later on day 2, a large tent has been erected, the park is filling with refugees and their belongings, and the fire is much closer. The houses at 1812/1814 Gough again appear at the right edge. Just left of the woman's white blouse is 1919 Sacramento, still standing in 2020.
Steve's SF postcard pages: