Could never find a pseudocode or proof for loess - it's apparently an approach, not a specific implementation.
If it might be helpful, we did some initial research about LOESS/LOWESS implementations for MetricsGraphics:
It may be possible to find a proof or citation from one of the existing implementations.
The following articles might be helpful for a reference LOWESS implementation, coming from William S. Cleveland:
Also, the following article might be useful: