The rheology of self-assembled elongated iron oxyhydroxide (FeOOH) and spherical silica (SiO2) particles in hexagonal (H-1) liquid crystal (LC) phase of water and non-ionic surfactant C12E9 is investigated by varying particle concentration and cooling rate. The rheology data shows that both SiO2/H-1 and FeOOH/H-1 LC composites exhibit a higher G' when compared to the particle-free H-1 phase, with increasing particle loading and cooling rate. FeOOH particles improve G' of the H-1 phase more significantly than SiO2 particles due to the formation of an interconnected network at H-1 domain boundaries at cooling rates of (1) and 2 degrees C/min. We hypothesize that self-assembly of particles at domain boundaries leads to a decreased mobility of defects causing an increase in elasticity of particle-laden H-1 phase. Dynamic strain sweep and creep experiments show a non-linear stress-strain relationship attributed to the alignment of micellar cylindrical rods under shear.