Doping ferroelectric Hf0.5Zr0.5O2 with La is a promising route to improve endurance. However, the beneficial effect of La on the endurance of polycrystalline films may be accompanied by degradation of the retention. We have investigated the endurance - retention dilemma in La-doped epitaxial films. Compared to undoped epitaxial films, large values of polarization are obtained in a wider thickness range, whereas the coercive fields are similar, and the leakage current is substantially reduced. Compared to polycrystalline La-doped films, epitaxial La-doped films show more fatigue but there is not significant wake-up effect and endurance-retention dilemma. The persistent wake-up effect common to polycrystalline La-doped Hf0.5Zr0.5O2 films, is limited to a few cycles in epitaxial films. Despite fatigue, endurance in epitaxial La-doped films is more than 1010 cycles, and this good property is accompanied by excellent retention of more than 10 years. These results demonstrate that wake-up effect and endurance-retention dilemma are not intrinsic in La-doped Hf0.5Zr0.5O2.