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We report a comprehensive spectro-polarimetric study of the black hole binaryLMC X$-3$ using simultaneous {\it IXPE}, {\it NICER} and {\it NuSTAR}observations in 0.5$-$20 keV energy band. The broad-band energy spectrum(0.5$-$20 keV) with {\it NICER} and {\it NuSTAR} is well described by the discemission of temperature $\sim$1.1 keV and a weak Comptonizing tail beyond$\sim$10 keV. This evidently suggests a disc-dominated spectral state of thesource with disc contribution of $\sim$96\%. The lack of variability($rms$$\sim$0.5\%) in the power spectrum further corroborates the high/softnature of the source. A significant polarization degree (PD) of 3.04$\pm$0.40\%(>7$\sigma$) at a polarization angle (PA) of$-$44.24$^{\circ}$$\pm$3.77$^{\circ}$ (>7$\sigma$) is found in 2$-$8 keV energyrange of {\it IXPE}. In addition, PD is seen to increase with energy up to$\sim$4.35$\pm$0.98\% (>3$\sigma$) in 4$-$8 keV band. Further, we attempt toconstrain the source spin ($a_{*}$) using broad-band spectral modelling thatindicates a weakly rotating `hole' in LMC X$-3$ with$a_{*}=0.273_{-0.012}^{+0.011}-0.295_{-0.021}^{+0.008}$ ($90\%$ confidence).Based on the spectro-polarimetric results, we infer that the polarization inLMC X$-3$ is resulted possibly due to the combined effects of the direct and/orreflected emissions from a partially ionized disc atmosphere. Finally, wediscuss the relevance of our findings.

First detection of X-ray polarization in thermal state of LMC X-3: Spectro-polarimetric study with IXPE