The painting is known to be a painting of the real life dog Ms. Honolulu (aka "Lulu"), the pet of Lost costume designer Roland Sanchez. Lulu originally belonged to executive producer Jack Bender, whose daughter Sophie rescued her from the Honolulu Humane Society.
The painting, titled Jacob's Dog, was in real life created by artist Thomas Hannsz, who also is among the Others background cast. Hannsz was able to create the painting because he happened to be the caretaker of Lulu while Bender was away or on the set. It is unknown if the prop used in the filming of Lost was a print that was artificially aged, or if the lighting and post-production alone resulted in its yellowish appearance.