Hi Pierre,
ArcGIS doesn't support the southing-westing axes of the Lo system. We added some "pseudo" definitions that work by using a negative scale factor (changing the signs on all coordinates). Are you using one of those?
Could this data already have changed/flipped values? If you are using one of the existing Lo coordinate systems, what happens if you redefine the coordinate system again by modifying the scale factor? Just change its sign.
Melita