The combination of lime with natural pozzolans for the production of binders in masonry construction dates back to ancient times. These were largely ignored with the industrialization of the building sector even though their use for specific applications is of interest. The use of lime-pozzolan binders with the least amount of lime is a relevant opportunity to reduce carbon emissions due to the decarbonation of limestone for the production of quicklime but also to introduce new alumino-silicate materials. In this context, the present investigation intends to relate marine dredged sediment to pyroclastic materials and to mix it with hydrated lime without any thermal treatment but after micronization. The blends were moist cured either at 20 °C or 50 °C and the paper will discuss the pozzolanic reactivity through the study of compressive strength and reaction kinetics from 3 days to 180 days. Reaction product assemblage, microstructure, and porosity refinement were also addressed after advanced curing ages. Results have well illustrated the long-term pozzolanic reactivity of the marine sediment cured at 50 °C through the whole combination of initially available lime after 60 days and the compressive strength development providing 12 MPa after 180 days.