"Lebensmittel" more represents something like "Life implement" or "means of life".
Edit:
Conceptually it maps almost exactly to Latin "nutrimentum", and hence, English "nourishment".
As such, I supposed we could construct some neo-latin from it to more closely approximate it, such as vitimentum or rather vitalimentum - but if you look closely at vitalimentum, you'll notice it contains "alimentum" as a substring, and, well:
Edit: Conceptually it maps almost exactly to Latin "nutrimentum", and hence, English "nourishment".
As such, I supposed we could construct some neo-latin from it to more closely approximate it, such as vitimentum or rather vitalimentum - but if you look closely at vitalimentum, you'll notice it contains "alimentum" as a substring, and, well:
https://en.wiktionary.org/wiki/aliment#Etymology