|Image from Wikipedia|
There are two really interesting images of the statue's carvings on a site called Darwaza, which looks at "global design history". The images on this site show the location of the carvings on the lion and a drawing of the carvings displaying the Runes, which appear to be the younger Futhark.
While the carving on the left shoulder does have a nice curve to it, the engraving on the right shoulder is particularly intricate, in a long swirling dragon.
Although the carvings date to the mid-eleventh century, they went unnoticed until the late 1700s, when Swedish-born diplomat and orientalist Johan David Åkerblad noticed them. Since their discovery, there have been many attempts to decipher their meaning, but centuries of pollution and weathering (erosion caused by rain, wind and other forces), have made the Runes hard to decipher.
The engravings appear to be an account the whereabouts of those involved in fighting and battles in the region. Even though the Greeks forbade it, at Harold the Tall's request, someone named Asmund "cut these runes". With him were Thorleif, Thord and Ivar. That is the left shoulder carving.
The right side is not only more intricate with its dragon shape, but the words being carved into that twisting dragon provide more insight into the events that transpired there. It appears as though the Asmund, who carved the other runes, helped Hakon, Ulf, and Örn conquer the port. As a result of their attempt to resist them, these vikings and Harold Hafi (another viking listed as imposing the fine, but not listed as one who secured the port) levied a large fine on the Greek people. The carving also states that Dalk (presumably another viking) is being held captive in some far off land and Egil and Ragnar are on an exhibition to Romania and Armenia.
These interpretations are from translations by Carl Christian Rafn, who was secretary for the Royal Society of Norse Antiquities. About sixty years after his translation, in 1914, Erik Brate, a renowned Swedish runologist did his own translation. Although it does not include all the names and locations as the first, it is considered to be more accurate. Moreover, this translation claims the Runes were carved in memory of Horsi, a good warrior that won gold in his travels. Both translations can be found on Wikipedia.
The Piraeus lion is one of four located at the Venetian Arsenal. So, if you're ever there look for the one with Runes carved into its shoulders. Look carefully, because weathering and pollution have made them difficult to spot, even when you know what you're looking for. There are also copies of the Piraeus Lion at the Swedish History Museum in Stockholm and the Piraeus Archeological Museum in Greece.