The structures of 15 La–Al–Si–O glasses, whose compositions span 11–28 mol% La2O3, 11–30 mol% Al2O3, and 45–78 mol% SiO2, are explored over both short and intermediate length-scales by using a combination of solid-state 27Al magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations. MAS NMR reveals Al speciations dominated by AlO4 groups, with minor but significant fractions of AlO5 (5–10%) and AlO6 (≲3%) polyhedra present in all La2O3–Al2O3–SiO2 glasses; the amounts of Al[5] and Al[6] coordinations increase for decreasing molar fraction of Si. The MD simulations reproduce this compositional trend, with the fractional populations of AlOp groups (p = 4, 5, 6) according well with the experimental results. The modeled La speciations mainly involve LaO6 and LaO7 polyhedra, giving a range of average La3+ coordination numbers between 6.0 and 6.6; the latter increases slightly for decreasing Si content of the sample. Besides the expected bridging and non-bridging O species, minor contributions of oxygen triclusters (≤9%) and free O2− ions (≤4%) are observed in all MD data. The glass structures exhibit a pronounced Al/Si disorder; the MD simulations reveal essentially random SiO4–SiO4, SiO4–AlOp and AlOp–AlOq (p, q = 4, 5, 6) associations, including significant amounts of AlO4–AlO4 contacts, regardless of the nAl/nSi molar ratio of the glass. The strong violation of Al[4]–Al[4] avoidance is verified by 2D 27Al NMR experimentation that correlates double-quantum and single-quantum coherences, here applied for the first time to aluminosilicate glasses, and evidencing AlOp–AlOq connectivities dominated by AlO4–AlO4 and AlO4–AlO5 pairs. The potential bearings from distinct fictive temperatures of the experimental and modeled glass structures are discussed.