Friedrich, † 1060 ⚭ 1056 Gertrud, Tochter des Grafen Konrad von Haldensleben, † 1116
1. Hedwig ⚭ Graf Gebhard von Supplinburg, † 1075, ⚭ Herzog Dietrich von Oberlothringen, † 1115
1. Kaiser Lothar, 1125–1137
2. Ida, † 1138 ⚭ Graf Sieghard X. von Burghausen, † 1104
3. Simon, Herzog von Lothringen
https://de.wikipedia.org/wiki/Grafschaft_Formbach
Hedwig von Formbach, daughter of Frederick and Gertrud von Haldensleben ; ⚭ probably I Count Heinrich; ⚭ II Gerhard of Süpplingenburg (X June 9, 1075 at Homburg ), 1062 Count in Harzgau ( Supplinburger ); Di III Dietrich , from 1090 Duke of Oberlothringen († 30 December 1115 ) ( House Châtenois ) - Hedwig of Formbach is therefore the mother of Emperor Lothar III.
https://de.wikipedia.org/wiki/Grafschaft_Formbach
Trying to find a Medlands entry...
1. LOTHAR von Süpplingenburg, son of GERHARD von Süpplingenburg Graf [im Harzgau] & his wife Hedwig von Formbach ([1/8] Jun 1075-Breitenwang am Loch, Tirol 4 Dec 1137, bur Königslutter). He was invested as LOTHAR Duke of Saxony in 1106 by Heinrich V King of Germany after the death of Magnus Billung Duke of Saxony. Duke Lothar immediately sought to build-up his lordship, triggered in 1112 the intervention of the emperor to whom he submitted in 1114. The dispute culminated in the defeat of the imperial army by the Saxons at Welfesholz in 1115[492]. He was elected as LOTHAR III King of Germany at Mainz 24 Aug 1125, largely through the manœuvrings of Adalbert Archbishop of Mainz and because he was seen by the German nobility as less of a dynastic threat than his main rival Friedrich II Duke of Swabia [Staufen][493]. He was crowned 13 Sep 1125 at Aachen. In 1130, King Lothar became embroiled in the dispute between rival Popes Anacletus II and Innocent II, in the hope of securing a return to the full right of lay investiture. He was crowned Emperor at the Lateran in Rome 4 Jun 1133 by Pope Innocent II, as Pope Anacletus II was occupying St Peter's[494]. He conceded the Pope's ownership of the lands previously held by Matilda Ctss of Tuscany, in return for a usufruct over them, and installed his son-in-law Heinrich "der Stolze" Welf Duke of Bavaria to govern these territories[495]. Following Roger II King of Sicily's expulsion of Pope Innocent II from Rome, Emperor Lothar launched an expedition to Italy in 1136. King Roger offered peace negotiations after the army took Benevento and Bari, but jurisdictional disputes broke out between the emperor and the Pope and the army returned to Germany, Emperor Lothar dying en route[496]. http://fmg.ac/Projects/MedLands/GERMANY,%20Kings.htm
I've cleaned it up to this - from the wikipedia article and the little on Medlands:
Hedwig von Formbach (c1058 -c1090), heiress to Süpplingenburg Castle.
Parents: Frederick, count of Formbach & Gertrude of Haldensleben
x Gerhard von Süpplingenburg Graf im Harzgau
*Lothar von Süpplingenburg becomes Lothar III King of Germany ([1/8] Jun 1075-Breitenwang am Loch in Tirol 4 Dec 1137, bur Königslutter)
*Ida (d.1138) x who married Sighard IX (d.1104)
xx Theodoric II, Duke of Lorraine
*Simon (1076 – 1138), who succeeded Theoderic as Duke of Lorraine x Adelaide of Leuven (d. 1158), daughter of his stepmother Gertrude and Henry III, Count of Leuven.
*Gertrude (who later changed her name to Petronilla) (d 1144) x Floris II of Holland
Sources:
http://fmg.ac/Projects/MedLands/SAXONY.htm#Lothardied1137
https://en.wikipedia.org/wiki/Hedwig_of_Formbach