The sphynx in the painting it not the famous Great Sphynx that sits near the Great Pyramid. There were many sphynx in Egypt at the time–it was a common “icon” of Egyptian religion and culture.
The head of the Great Sphynx is disproportionate because as the body was being carved a fault was found in the stone, so, in order to keep the stone from cracking, the body was made larger, thus bypassing the crack and making the statue more stable. I’ve heard the theories that it was once a lion’s head carved down to a human head, but there is no real evidence for that.
I guess the picture I linked isn’t the one being asked about in this thread, still I think it’s a lovely depiction of the Holy Family as they rested on their flight into Egypt with Mary and the Child asleep in the sphynx’s paws–a symbol of the prophecy “I called my son out of Egypt” and with St. Joseph sleeping close at hand, chastely guarding the Mother and Christ Child. I have a copy of this painting displayed on our bedroom wall along with one of Our Lady of Mount Carmel loving holding Jesus in her arms. Love both pictures and what they symbolize.