Shushannah Walshe has a piece at the Daily Beast floating the possibility that, if Lisa Murkowski does indeed lose to Joe Miller, she could run as a third-party candidate. Walshe refers to an unnamed source within the Murkowski campaign who says that they plan to "see whether the option is there or not, but it's a decision she (Murkowski) has to make. There is an option I know of."
Walshe suggests two possibilities: running as a write-in candidate, which would be extremely difficult, expensive, and unlikely; or running on the Alaska Independence Party's ticket. Walshe seems to think Murkowski's campaign is considering the latter, despite the trouble she might have overcoming the party's secessionist bent.
But Gail Fenumiai, director of Alaska's Department of Elections, told me in an email that Murkowski would not be able to run on the AIP's ticket. "There were no US Senate Alaskan Independence Party candidates on the Primary Election," Fenumiai wrote, "so there is no option for them to place someone on the ballot."
Since Murkowski missed the June filing deadline for independent candidates, her main other third-party option, other than running as a write-in, seems to be with the state's Libertarian Party. Fenumiai said that the party could replace its current candidate with Murkowski if it so chooses.