Kammerer et al. (arXiv link) show that LIFE would also be a powerful mission to search for Earth-like planets around Sun-like stars. This is important because the true habitability of habitable zone (HZ) planets around M-dwarfs is still an open question and previous LIFE yield estimates had shown a strong preference for detections around M-dwarfs. We also present, for the first time, a mission parameter study that shows how the expected yield of HZ planets depends on the assumed mirror diameter, total throughput, median exozodiacal dust level, and accessible wavelength range. We find that to detect a statistically relevant sample of ~30 planets within the optimistic HZ of Sun-like stars, a mission with larger 3 m mirrors (with 5% throughput) or higher 20% throughput (with 2 m mirrors) is required. These requirements are relaxed when extending the scope to the entire sample of FGK-type stars.