After the discovery of space masers based on OH radicals (Weaver et al. 1965) and H2O (Cheung et al. 1969) such microwave lasers have been found to work in more than 100 molecular species (Elitzur 1992; Townes 1997), as well as in highly excited H atoms (Strelnitski et al. 1996). In the IR region (10 µm), the effect of stimulated emission of radiation in the CO2 molecule has been discovered in the Martian and Venus' atmospheres (Betz et al. 1976; Mumma et al. 1981). We report here on the discovery of laser action in the range 0.9-2 µm in several spectral lines of Fe II, which are associated with transitions from "pseudo-metastable" states populated by spontaneous transitions from Lyα pumped Fe II levels. The intense Lyα radiation is formed in the HII region of gas condensations close to the star η Car. The laser transitions form together with spontaneous transitions closed radiative cycles, one of which includes the extremely bright 2507/09 A lines. Closed radiative cycles, together with an accidental mixing of energy levels, may provide an explanation of the abnormal intensities of these UV non-lasing lines. Using the complicated energy level diagram of Fe II we present those peculiar features, which are essential for the inverted population and laser effect: the pumping, the level mixing, and the "bottle neck" for spontaneous decay. The laser action is a new indicator of non-equilibrium and spatially non-homogeneous physical conditions as well as a high brightness temperature of Lyα in ejecta from eruptive stars. Such conditions are very difficult to probe by existing methods, and we propose some future experiments. The fact, that the lasing near-IR lines appear in the spectrum with about the same intensity as non-lasing lines is discussed and compared with the situation in masers.