Efficient and cost-effective Si-compatible lasers are a longstanding wish of the optoelectronic industry. In principle, there are two options. For many applications, lasers based on III-V compounds provide compelling solutions, even if the integration is complex and therefore costly. However, where low costs and also high integration density are crucial, group-IV-based lasers - made of Ge and GeSn, for example - could be an alternative, provided their performance can be improved. Such progress will come with better materials but also with the development of a more profound understanding of their optical properties. In this work, we demonstrate, using Ge microbridges with strain up to 6.6%, a powerful method for determining the population inversion gain and the material and optical losses of group IV lasers. This is done by deriving the values for the injection carrier densities and the cavity losses from the measurement of the change of the refractive index and the mode linewidth, respectively. We observe a laser threshold consistent with optical gain. Material loss values are obtained from a tight-binding calculation. Lasing in Ge - at steady-state - is found to be limited to low temperatures in a narrow regime of tensile strain at the crossover to the direct-band-gap band structure. We explain this observation by parasitic inter-valence-band absorption that increases rapidly with higher injection densities and temperature. N-doping seems to reduce the material loss at low excitation, but it does not extend the lasing regime. We also discuss the impact of the optically inactive carriers in the L-valley on the linewidth of group IV lasers.