The atomic-level structure of metallic glasses (MGs) is one of the most fundamental and challenging topics in condensed matter physics. Unlike crystalline metals or alloys, the MGs are lacking in a well-defined description of structure order, which is a major obstruction for relating its structure to physical properties. Obviously, it is vitally important to have an in-depth understanding of the atomic packing scheme in MGs. Due to the limitations of experimental characterization methods, it is hard to obtain the atomic packing scheme of MGs in experiment. Computational simulation on an atomic scale has become an important method of characterizing the atomic structure of MGs. The La-based LaNiAl glass forming system is well-known for its good glass-forming ability, distinctive relaxation peak that is well separated from relaxation, and liquid-liquid transition at a temperature around 1000 K. Many efforts have been made to investigate these novel properties. However, the atomic structure of this system is rarely studied. In this paper, the atomic structure evolution from liquids to glass states in La-based binary MGs La65Ni35 and La65Al35 are studied via ab initio molecular dynamics based on the density functional theory. The local structures are systematically analyzed by the radical distribution function, partial radical distribution function (PRDF), Voronoi tessellation method, and bond-type method in Honeycutt-Andersen. The results indicate that the PRDF of NiNi is much weaker than that of AlAl, which indicates the NiNi avoidance in La65Ni35. The major peaks of PRDFs are always smaller than the sum of efficient radius of the two kinds of atoms, especially for LaNi pairs. Atomic structure of the two systems are coincident with dense atomic packing scheme and the difference between major Voronoi polyhedron types (0, 3, 6, 0 for La65Ni35 and 0, 2, 8, 1, 0, 2, 8, 0 for La65Al35) in local structures is controlled by their ratio of solute to solvent atomic size. The high five-fold local symmetry structure gradually increases in both systems with the decrease of temperature, which validates its pivotal part in hindering crystallization. The electronic structure is studied with the partial density of states. It is found that the significant bond-shortening between La and Ni is due to the strong hybridization between Ni-3d and La-5d electrons and this result may play a key role in understanding composition related structure and properties in MGs.