Context : Massive stars , although being important building blocks of galaxies , are still not fully understood . This especially holds true for Wolf-Rayet ( WR ) stars with their strong mass loss , whose spectral analysis requires adequate model atmospheres . Aims : Following our comprehensive studies of the WR stars in the Milky Way , we now present spectroscopic analyses of almost all known WN stars in the LMC . Methods : For the quantitative analysis of the wind-dominated emission-line spectra , we employ the Potsdam Wolf-Rayet ( PoWR ) model atmosphere code . By fitting synthetic spectra to the observed spectral energy distribution and the available spectra ( ultraviolet and optical ) , we obtain the physical properties of 107 stars . Results : We present the fundamental stellar and wind parameters for an almost complete sample of WN stars in the LMC . Among those stars that are putatively single , two different groups can be clearly distinguished . While 12 % of our sample are more luminous than 10 ^ { 6 } L _ { \odot } and contain a significant amount of hydrogen , 88 % of the WN stars , with little or no hydrogen , populate the luminosity range between \log ( L / L _ { \odot } ) = 5.3 ... 5.8 . Conclusions : While the few extremely luminous stars ( \log ( L / L _ { \odot } ) > 6 ) , if indeed single stars , descended directly from the main sequence at very high initial masses , the bulk of WN stars have gone through the red-supergiant phase . According to their luminosities in the range of \log ( L / L _ { \odot } ) = 5.3 ... 5.8 , these stars originate from initial masses between 20 and 40 M _ { \odot } . This mass range is similar to the one found in the Galaxy , i.e . the expected metallicity dependence of the evolution is not seen . Current stellar evolution tracks , even when accounting for rotationally induced mixing , still partly fail to reproduce the observed ranges of luminosities and initial masses . Moreover , stellar radii are generally larger and effective temperatures correspondingly lower than predicted from stellar evolution models , probably due to subphotospheric inflation .