Highly disordered amorphous Li7La3Zr2O12 (aLLZO) is a promising class of electrolyte separators and protective layers for hybrid or all-solid-state batteries due to its grain-boundary-free nature and wide electrochemical stability window. Unlike low-entropy ionic glasses such as LixPOyNz (LiPON), these medium-entropy non-Zachariasen aLLZO phases offer a higher number of stable structure arrangements over a wide range of tunable synthesis temperatures, providing the potential to tune the LBU-Li+ transport relation. It is revealed that lanthanum is the active "network modifier" for this new class of highly disordered Li+ conductors, whereas zirconium and lithium serve as "network formers". Specifically, within the solubility limit of La in aLLZO, increasing the La concentration can result in longer bond distances between the first nearest neighbors of Zr─O and La─O within the same local building unit (LBU) and the second nearest neighbors of Zr─La across two adjacent network-former and network-modifier LBUs, suggesting a more disordered medium- and long-range order structure in LLZO. These findings open new avenues for future designs of amorphous Li+ electrolytes and the selection of network-modifier dopants. Moreover, the wide yet relatively low synthesis temperatures of these glass-ceramics make them attractive candidates for low-cost and more sustainable hybrid- or all-solid-state batteries for energy storage.