You may want to check out the thread ArcHydro Problem Solvers and see if there is an answer there.
I'm not familiar with this particular error. The error message seems to point to the grid, though in the geoprocessing, the tool may convert vector data to a grid, so I can't say for sure if it is the grid you input, or a temporary grid.
The inputs to the LongestFlowPath tool are a Drainage Area (polygon) and Flow Direction Grid (grid).
Check your inputs to make sure they are correct.
Check your inputs to make sure they are in the right projection.
Check you processing extents to make sure they cover the processing area.