I'll bet Life's Rich Tapestry is an ironic (in that classical British ha-ha-only-serious way) emphatic restatement of the phrase the tapestry of life.
Which in turn may come from the German phrase der Teppich des Lebens. At this point I have to guess that the German phrase might have been coined by Stefan George, an influential neoclassical lyrical symbolist German poet of the late 19th century; he wrote a book of poems called Der Teppich des Lebens und die Lieder von Traum und Tod mit einem Vorspiel (The Tapestry of Life and The Song of Dream and Death in One Act).