Full potential-linearised augmented plane wave (FP-LAPW) method is used to study the structural, electronic, half-metallic and optical properties of Ba$_2$LuTaO$_6$ doped with d-block atoms Co, Fe, Mn and Cr using density functional theory (DFT) technique. Ba$_2$LuTa$_{0.75}$TM$_{0.25}$O$_6$ supercells were constructed by doping 3d transition metal atoms Co, Fe, Mn and Cr with 2.5% of concentration in Ba$_2$LuTaO$_6$ host compound. The possibility of half-metallic ferromagnetism in Ba$_2$LuTa$_{0.75}$TM$_{0.25}$O$_6$ (TM = Co, Fe, Mn and Cr) was analysed by electronic band structure and density of state calculations. We found that Ba$_2$LuTa$_{0.75}$(Co and Cr)$_{0.25}$O$_6$ alloys exhibit complete half-metallic characteristics with a total spin moment of 2.00 and 1.00 $\mu_B$ and direct band gap of $Eg ↑= 0.52$ eV and $Eg ↓= 1.60$ eV, respectively. These results may be of interest for spintronics applications. Moreover, the optical properties of the material in question are also examined and discussed.