While Alison's father's family is primarily Irish, most people named Shaffer in the United States are of German descent. Shaffer usually comes from German Schaefer "shepherd" or Schaffer "steward" or "baliff". Because Pennsylvania has such a large population from Germany, more Shaffers are found there than anywhere else. While it's possible that, in Alison's case, Shaffer is actually from an Irish name, I could not find any matches.
If the name is from Schaefer, it literally means "sheeper" (cognate with English sheep.) Sheep is one of those words found only in Germanic languages, with an unknown origin; it may have meant "something protected". If it is from Schaffer it literally means "shaper" (cognate with English shape), and goes back to Proto Indo European skepr, "cutter, carver, creator".
Spiritually, Shaffer begins with a shielding, protective energy, which is broken open and releases into freedom and motion.
The name has several potential origins, all of which may be partly true.
One theory, which I heard from others in my family when I was young, is that the name came from Lille, a city in northern France (originally called L'Isle, "the island", since it was built on a hill in the midst of a marsh). Around 900 AD, Lille and other areas in northern France were invaded by Vikings, who pillaged the area and then conquered and settled it. In 1066, the lords of Lille most likely joined William of Normandy in his invasion of England, and were given lands there as a reward. The English version of the French name Lille would have been Lilly. However, I have some doubt that this origin is true, since it happens that in 1066 the town was referred to in a charter as "Isla" (medieval Latin for "island"). This may just be because the charter was written in Latin; but to me it seems doubtful that in 1066 the name of the city had already been shortened to Lille. Any lords from there would not have anglicized the name as "Lilly".
But the name Lilly is found in two main areas in England: Berkshire and Hertfordshire. The Berkshire Lillys take their name from Old English Lillingleah, meaning "Lilla's glade". (The name "Lilla" was a personal name in Old English; it may mean "little". A glade is a woodland clearing.) The Hertfordshire Lillys are derived from Old English Linleah, "flax-glade". (Note that the word leah, "glade", is the origin and meaning of Alison's middle name, Leigh.)
In any case, however much I might wish it, the surname Lilly does not seem to be historically related to the flower name lily. That name goes back to Greek leirion, possibly borrowed from Egyptian word for the plant, hlile.
The name is full of L's, a sound of light and fluidity, as well as the notions of volume and depth. The initial 'i' sound indicates stasis, ice, stillness; the release into the second 'i' is high, tense energy.