After all this, you might think so more research is worthwhile. No one says Medlands is the final authority on anything.
So, the second thing you could do is check Wikipedia. Wikipedia is far less reliable than Medlands, but Wikipedia has the advantage that it might lead to other quality sources.
And, bear in mind here that Wikipedia often provides a good balance to Medlands. Medlands doesn't have everything and Wikipedia has too much. Wikipedia's primary fault is that it often has bad relationships because it isn't using quality sources.
When I check Wikipedia, I always check 3 different versions. That helps offset the problems. For someone like Liudolf, I would normally check English Wikipedia, German Wikipedia, and French Wikipedia.
English Wikipedia says Liudolf was son of Markgraf Brun or Brunhart and his wife Gisla von Verla. It cites German Wikipedia.
https://en.wikipedia.org/wiki/Liudolf,_Duke_of_Saxony
German Wikipedia says "Liudolfs Abkunft ist nicht sicher zu bestimmen. Seine Eltern sollen der historisch sonst nicht fassbare Markgraf Brun (oder Brunhard) der Jüngere, seine Mutter dessen Frau Gisla von Verla sein. Nach anderen Quellen hieß seine Mutter Addida und war eine Tochter des sächsischen dux Ekbert und der Heiligen Ida von Herzfeld ."
-- Liudolf is supposedly son of an elusive Markgraf Brun by Gisla von Verla, but also said to be son of Addida, a woman whose father was Ekbert (the man Medlands identified as son of the earlier Bruno. (Also, Liudolf is considered to be the progenitor of this family, which means he is the earliest certain ancestor.)
https://de.wikipedia.org/wiki/Liudolf_(Sachsen)
French Wikipedia gives Liudolf's wife and children but no mention of his parents or ancestry except to say he is the earliest documented ancestor of this family.
https://fr.wikipedia.org/wiki/Liudolf_de_Saxe
So, we see a couple of things. Taken together, these articles show us there is no firm information about Liudolf's ancestry. Just as Medlands said.