From what I could find the Duchy of Lothier covered that particular area of the lowlands. The counties of Artois and Flanders are still there. Here is a good link to help show it a bit clearer
The problem is that there never existed a duchy of Lothier in France (or at least I have never heard of one). From what I could find, it refers either to a deformation of
Lower Lothringia, which is Lower Lorraine or the duchy of Brabant, and neither of those comprise the lands of Artois and Flanders (I mention those two because they are the biggest in the area and would have seemed like the natural choice for the ''duchy'' level lands), or the region of Picardie.
Moreover, none of the maps I found actually name this region Lothier or anything similar...
This seems to be the divisions of the region.
As you can see, Artois, Boulogne and Flanders seem to be the biggest titles in the region and aren't close to the lands of Lower Lothringia, and so would seem to be the best choice for duke-level holdings, no?
Also : why does Angoulême comprise the Saintoge, for practical purposes? And what is the big red land next to Burgundy that comprises lands of the Dauphiné, Franche-comté, Provence, etc.?