We report on the performance of AlGaN-based deep ultraviolet light-emitting diodes (UV-LEDs) emitting at 265 nm grown on stripe-patterned high-temperature annealed (HTA) epitaxially laterally overgrown (ELO) aluminium nitride (AlN)/sapphire templates. For this purpose, the structural and electro-optical properties of ultraviolet-c light-emitting diodes (UVC-LEDs) on as-grown and on HTA planar AlN/sapphire as well as ELO AlN/sapphire with and without HTA are investigated and compared. Cathodoluminescence measurements reveal dark spot densities of $3.5\times {10}^9{\mathrm{cm}}^{?2}$, $1.1\times {10}^9{\mathrm{cm}}^{?2}$, $1.4\times {10}^9{\mathrm{cm}}^{?2}$, and $0.9\times {10}^9{\mathrm{cm}}^{?2}$ in multiple quantum well samples on as-grown planar AlN/sapphire, HTA planar AlN/sapphire, ELO AlN/sapphire, and HTA ELO AlN/sapphire, respectively, and are consistent with the threading dislocation densities determined by transmission electron microscopy (TEM) and high-resolution X-ray diffraction rocking curve. The UVC-LED performance improves with the reduction of the threading dislocation densities (TDDs). The output powers (measured on-wafer in cw operation at 20 mA) of the UV-LEDs emitting at 265 nm were 0.03 mW (planar AlN/sapphire), 0.8 mW (planar HTA AlN/sapphire), 0.9 mW (ELO AlN/sapphire), and 1.1 mW (HTA ELO AlN/sapphire), respectively. Furthermore, Monte Carlo ray-tracing simulations showed a 15% increase in light-extraction efficiency due to the voids formed in the ELO process. These results demonstrate that HTA ELO AlN/sapphire templates provide a viable approach to increase the efficiency of UV-LEDs, improving both the internal quantum efficiency and the light-extraction efficiency.