Description
The Least Cost Path tool accumulates positive values across the Input Cost Surface. NoData values cannot be crossed and will be avoided. However, if there is no path around NoData pixels, no solution (output path) will be provided.
Solution
Review the Input Cost Surface for NoData values between the Input Starting Point and the Input Ending Point. Either update these pixels, or change the starting and ending points.
Optionally, if the NO_DATA option was used, try the SMALL_POSITIVE option instead. This will convert NoData pixels to a very small positive number (0.0000001).