Wow!! That certainly looks like Grace Church. Note that Grace Church is on the East side of Broadway, so that the procession would be moving downtown towards City Hall.
When my father was admitted to the Bar in 1948 or 1949, CC Burlingham, who had sponsored his admission, took him to lunch and recalled having witnessed Lincoln's funeral procession in NY. CC could still remember the different brigades that marched, including how they were dressed and the like. He was close to 100 at the time.