Lime Based Mortar became very popular due to its outstanding features of flexibility, permeability and low carbon emissions. However, lime’s characteristic delayed setting, late hardening time, low mechanical strength, among others, overshadowed significance of its outstanding features, thereby putting its overall use into decline, particularly, with the 19th century Portland Cement discovery. This study therefore aims at reviving lime usage through a sustainable lime composite, by integrating an industrial by-product, Ground Granulated Blast Furnace Slag (slag) with lime, in form of lime-slag mortar, with a view to reducing the mortar thermal conductivity. The methodology involved mortars with the same Binder/Aggregate (B/A) mix ratio (1:3) using five separate volumetric compositions of ‘slag-lime’ binders (i.e. 1:1, 1:2, 1:3, 2:1 and 3:1). Physical properties of the mortars involving their Water/Binder (W/B) ratios, Air Contents and Bulk Densities were recorded. Comparative evaluations of the compositions in hardened state, involving thermal conductivities were carried out at specific intervals through a twelve-month curing period. These were partly monitored through assessments of the composites’ microstructural behaviours over a six-month period. Results of the investigation show that addition of slag to mortars facilitate slightly larger pores with increased porosities. However, these effects are minimal (i.e. from 23.42% to 25.37% porosity) when slag content is at equal volumetric content with lime. A general reduction (not in a linear trend) in the thermal conductivities of the mortar with increasing slag content was observed, cumulating in 25% decrease in the composites having thrice volumetric content of slag, relative to lime. Composite’s reduced thermal conductivity would be of utmost importance in construction especially, where material’s limited thermal conductivity property is of utmost importance.