Context. Lithium plays a crucial role in probing stellar physics, stellar and primordial nucleosynthesis, and the chemical evolution of the Galaxy. Stars are considered to be the main source of Li, yet the identity of its primary stellar producer has long been a matter of debate. Aims. In light of recent theoretical and observational results, we investigate in this study the role of two candidate sources of Li enrichment in the Milky Way, namely asymptotic giant branch (AGB) stars and, in particular, novae. Methods. We utilised a one-zone Galactic chemical evolution (GCE) model to assess the viability of AGB stars and novae as stellar sources of Li. We used recent theoretical Li yields for AGB stars, while for novae we adopted observationally inferred Li yields and recently derived delay time distributions (DTDs). Subsequently, we extended our analysis by using a multi-zone model with radial migration to investigate spatial variations in the evolution of Li across the Milky Way disc and compared the results with observational data for field stars and open clusters. Results. Our analysis shows that AGB stars clearly fail to reproduce the meteoritic Li abundance. In contrast, novae appear as promising candidates within the adopted framework, allowing us to quantify the contribution of each Li source at the Sun’s formation and today. Our multi-zone model reveals the role of the differences in the DTDs of Type Ia supernovae and novae in shaping the evolution of Li in the various galactic zones. Its results are in fair agreement with the observational data for most open clusters, but small discrepancies appear in the outer disc.