The rim seems to have a lower lip. The face is deeper than the average penny from the high point on the rim. Also the top part of "United States" was struck on/close to the edge/lip. Coin is 2000-P.
Look at the coin closely, in particular what you call the lower lip of the rim and the rim directly opposite that. At 6 o'clock you have the line (lower lip) on the rim. At 12 o'clock the rim is extremely narrow, not even all there. These uneven rims occur when a coin is not centered well when struck. A well centered coin has equal sized rims all the way around, a coin not well centered doesn't. It is often caused by the dies being slightly misaligned. It is so common it even has its own name, MAD - misaligned die strike. A coin being well centered is one the criteria used to grade coins, but in this day and age it is largely forgotten except by those who really know how to grade.
I don't believe the OP is referring to the centering of the coin Doug. I think he';s referring to the "lip" on the inside of the rim. Mike Diamond wrote about this in a recent Collectors Clearinghouse in Coin World of which I cannot seem to locate at the present time.
Non_cents had the right answer. This is a form of die deterioration that the late Eric Von Klinger designated as a "ridge ring". It's common on copper-plated zinc cents.
