LC3 binders have been gaining interest from researchers but also from the construction industry, which is already developing products based on it. LC3 has one downside, however: its low early age strengths, compared to that of Portland cement. A mineral accelerator system (MAS) based on calcium aluminate is a potential solution to remedy this limitation. This paper will present the comparison of properties of LC3-based mortars containing the MAS and mortars prepared with conventional LC3 and CEM I, as well as with LC3 combined to conventional Portland accelerators, such as Na2CO3 and CaCl2. Were evaluated their compressive strength, structuration by the ultrasound method, and dimensional variations, followed by different techniques including the Ring Test method. The results showed that the MAS and the conventional accelerators lead to a faster structuration, reducing the LC3 setting time to less than 6 h. Their effects on the 24 h and later age strengths were not the same, however. While conventional admixtures have little impact on the early strengths of the LC3, the MAS increases them from the first hours. At the dosage used in this study, it was possible to reach the same one day strength as the CEM I. MAS also leads to an improvement of later age strengths, exceeding those of LC3 and CEM I. The acceleration brought by the MAS is robust to temperature and to Portland cement variations. Moreover, the addition of the MAS partially compensates for the chemical and drying shrinkages, making the mortar less prone to crack.