Lassa fever (LF), a viral hemorrhagic fever disease with a case fatality rate that can be over 20% among hospitalized LF patients, is endemic to many West African countries. Currently, no vaccines or therapies are specifically licensed to prevent or treat LF, hence the significance of developing therapeutics against the mammarenavirus Lassa virus (LASV), the causative agent of LF. We used in silico docking approaches to investigate the binding affinities of 2015 existing drugs to LASV proteins known to play critical roles in the formation and activity of the virus ribonucleoprotein complex (vRNP) responsible for directing replication and transcription of the viral genome. Validation of docking protocols were achieved with reference inhibitors of the respective targets. Our in silico docking screen identified five drugs (dexamethasone, tadalafil, mefloquine, ergocalciferol, and flunarizine) with strong predicted binding affinity to LASV proteins involved in the formation of the vRNP. We used cell-based functional assays to evaluate the antiviral activity of the five selected drugs. We found that flunarizine, a calcium-entry blocker, inhibited the vRNP activity of LASV and LCMV and virus surface glycoprotein fusion activity required for mammarenavirus cell entry. Consistently with these findings, flunarizine significantly reduced peak titers of LCMV in a multi-step growth kinetics assay in human A549 cells. Flunarizine is being used in several countries worldwide to treat vertigo and migraine, supporting the interest in exploring its repurposing as a candidate drug to treat LASV infections.