Lebensraum had a lot of its roots in the problems Germany encountered in WW1.
During the First World War, the Central Powers ran into major supply issues in many areas, arguably the most critical being food. Germany and Austria Hungary were dependent on food imports prior to WW1, and the British naval blockade was incredibly effective at cutting off the food supplies of the Central Powers. Further exacerbating the problem was the Russian invasion of Galicia in 1914, which was a prime food-producing region for Austria Hungary. The Central Powers suffered from major food shortages through the entirety of the war, and the situation by the end of the war had deteriorated in Austria that even metropolitan areas like Vienna were suffering from near-starvation level rations. The core of the issue was that neither Germany nor Austria Hungary were self-sufficient when it came to food, and thus they were incredibly vulnerable to blockade or even embargo.
As the war went on, Germany resorted to a lot of measures that serve as stepping stones for a lot of the ideals of Lebensraum. Chief among these is Ober Ost. Ober Ost was an occupation administration that ran German-occupied areas in the Baltic practically as colonies. They resorted to forced labor and requisitioned food, and the scale and severity of these tactics would increase as the war worsened for Germany. By the end of the war, the locals in Ober Ost were being kept on starvation rations and as much food as possible was being requisitioned for Germany proper, but to no avail - the German administration there never managed to make much of a "profit" when it came to the resources they hoped to gain from the region. Similar tactics would also be used in other German-occupied areas such as Belgium, although not to the scale or severity of Ober Ost. These problems also played a part in the creation of the occupied zone after the Treaty of Brest-Litovsk - the Central Powers were to occupy the majority of Ukraine, the hope being that the fertile region would be able to finally put an end to the food shortages at home.
Ultimately, despite Germany's fairly brutal efforts to break its dependency on foreign food imports during WW1, the regions they occupied always ended up being a drain on the German war effort rather than a net gain, especially when it came to food. Lebensraum as it took shape (and a lot of the more banal Nazi atrocities in the East) would largely serve as an extension of their practices in WW1 with the intention of finally making Germany resilient against a blockade or embargo. To that extent, they hoped for not only capture of large areas of food-producing land, but major reorganizations and colonizations of these regions in order to better orient them for meeting German wartime and long-term needs. Given that experience in WW1 showed that the existing populations in the East ultimately ended up being a drain on resources even when limited to the absolute bare minimum rations, the logical extension here was particularly brutal - forced labor from enough of the population to support colonization, and deportation or extermination of the remainder of the population. Fortunately, German efforts in WW2 did little better than WW1 despite being significantly more destructive. Germany suffered the same kinds of food shortages they experienced in WW1, and Germany was never able to establish the kind of agricultural base it hoped for in the East.