My Neighbor Totoro/WMG

The sandals that were found in the lake were Chihiro's sandals.

 * It was connected to the Kohaku river and (ko)Haku saved her and then the shoes drifted downstream until they eventually hit a pond. The river was then filled in years later.
 * Only problem is that the events of Totoro are occurring 1952-1956 (depending how you interpret the calendar behind the mom at the hospital) and Chihiro's time is shown to be contemporary 1990s. Kohaku River (the spirit) could easily be around that long and not age but it would make Chihiro at least in her 50s by the time of Spirited Away! And I do not think that you can stretch Spirited Away to occurring in the late 1950s - early 1960s because the technology was all wrong. The car was too modern for one thing.
 * Time flows strangely in the world of spirits. Perhaps Chihiro lost her shoe in the '90s, but it was found in a different time period.

Totoro is the far future of Avatar: The Last Airbender
All the talk about spirits and such? It all fits snuggly in with the world. Even more so with The Legend of Korra, so it may not even be all that far into the future.