Liudolf was in Italy, when the battle of Lechfeld took place and he caught malaria there. He would return to Germany but he'll most likely still pass away in 956.
I don’t think this is correct. In late 955 Liudolf is said to have been present at the Battle of Raxa against the Slavs, which took place right after Lechfeld. Thietmar records the death of Liudolf on September 6th 957 and writes that he died “after scarcely a year” in Italy, again strongly suggesting that he was still in Germany at the time of Lechfeld, which happened just over two years before his death.
If we then assume that Liudolf is still alive in this scenario, we may also safely assume that he does not launch his campaign in Italy as IOTL, because he first needs to secure the German crown. Although he’s the obvious favorite as the king’s eldest and only adult son, his path to the crown is not necessarily an easy one. Many of the kingdom’s magnates fought against him in his recent rebellion against Otto. His duchy of Swabia was stripped from him and given to Burchard. Liudolf was also accused of having conspired to “invite” the Magyars into the kingdom; even if there is no truth to this, it looks awfully convenient that immediately after his rebellion fails and he’s stripped of his duchy, the Magyars do his work for him by killing his father.
Otto’s young nephew Henry (OTL Henry II of Bavaria) may be Liudolf’s most serious opponent despite being a child. Even if the elder Henry of Bavaria still dies in late 955, Bavaria will be ruled by his widow Judith of the historically rebellious Bavarian Luitpoldings, who is also the mother-in-law of Burchard of Swabia. Judith may make her peace with Liudolf or support the infant Otto “II,” but she may be more likely to support the claim of her own son on the basis that Liudolf is a traitor and the younger Otto is a newborn babe and the son of a foreign princess. If Burchard supports her - and perhaps also Hermann of Saxony, who is struggling against his pro-Liudolf nephews - she could potentially mount a very serious bid for the throne on Henry’s behalf. Having Arnulf the Bad’s daughter end up as regent of Germany would be an interesting twist of fate.
The Slavs will be an immediate problem. IOTL Otto defeated them at the Raxa two months after Lechfeld, but if Otto is dead and the kingdom is divided it may be difficult to amass a force sufficient to stop them. This uprising was allegedly encouraged by Wichmann and Egbert Billung, who hated Otto and had supported Liudolf’s rebellion. It’s possible that if Otto dies at Lechfeld they may not stir up the rebellion at all (I’m not certain of the exact sequence of events in 955), or they may still use the Slavs to try and overthrow their uncle Hermann in Saxony and support Liudolf’s claim to Germany. It may tarnish Liudolf even further if he is perceived as trying to gain the throne with the help of pagan Magyars and Slavs.
More broadly, Otto’s death doesn’t necessarily mean the end of the Italian ambitions of the German kings. Otto did not invent the idea of a German king conquering Italy and taking the imperial crown - Arnulf of Carinthia had done it, and IIRC Henry the Fowler was considering it at the time of his death. The conquest will be delayed by Otto’s death, particularly if the succession is bitterly contested, but whether it is actually averted depends substantially on whether Berengar II is able to consolidate his position in Italy, which has already been seriously compromised by Otto’s previous invasion. In the absence of a strong German king, Berengar’s Italian opponents will probably look elsewhere for a “savior,” perhaps to King Conrad of Burgundy. IOTL he showed little interest in Italian intervention, but this may be because he was overshadowed by (and on good terms with) Otto.