Alloy designs of light-weight high and medium entropy alloys (LW-HEA and LW-MEA, respectively) are discussed in relation to solving the problem of the empirical alloy parameter, ΔHmix, and the difficulties of the fabrication process. The ingots of newly-designed Al–Mg–Li–Ca LW-MEAs were fabricated by the conventional casting process via crucible melting without using a vacuum furnace, and casting under air atmosphere. The ΔHmix parameter is the average value of the mixing enthalpy of ΔHi-j between the two components, i-j, in the multicomponent alloys, and the dispersion of ΔHi-j cannot be evaluated. The parameter δ(ΔHmix) was suggested for the evaluation of the dispersion of ΔHi-j. The Al–Mg–Li–Ca LW-MEAs were designed based on the empirical alloy parameters, including δ(ΔHmix). The alloy ingots of equiatomic AlMgLiCa, non-equiatomic Al2MgLiCa, and AlMgLiCa0.3 were successfully obtained by the conventional casting process. The solidification microstructure of the ingots in the Al2MgLiCa LW-MEA was investigated, with particular focus on the position dependences of the chemical composition, constituent phases, solidification microstructure, and hardness. The present study clarified that LW-HEAs and LW-MEAs containing Al, Mg, Li, and Ca can be obtained by the conventional casting process under air atmosphere, without specific expensive casting equipment. This Paper was Originally Published in Japanese in J. JFS 91 (2019) 717–729. Minor corrections in abstract, main text, figure and table captions, and references were performed with translation from Japanese to English and proof reading by native speakers. Some references written in Japanese was replaced by the related references written in English: Ref. 11) was changed from “the 24th Committee on casting of Japan Society for the Promotion of Science (JSPS), Subcommittee on casting process, the 20th meeting document, No. 22 (2018) 1–5.” to “Mater. Des. 184 (2019) 108172”. Ref. 41) was changed from “J. Soc. Mater. Sci., Japan 68 (2019) 205–211.” to “Mater. Trans. 61 (2020) 311–317”.