The \text { Lyman - } \alpha forest 1D flux power spectrum is a powerful probe of several cosmological parameters . Assuming a \Lambda \mathrm { CDM } cosmology including massive neutrinos , we find that the latest SDSS DR14 BOSS and eBOSS \text { Lyman - } \alpha forest data is in very good agreement with current weak lensing constraints on ( \Omega _ { m } , \sigma _ { 8 } ) and has the same small level of tension with Planck . We did not identify a systematic effect in the data analysis that could explain this small tension , but we show that it can be reduced in extended cosmological models where the spectral index is not the same on the very different times and scales probed by CMB and \text { Lyman - } \alpha data . A particular case is that of a \Lambda \mathrm { CDM } model including a running of the spectral index on top of massive neutrinos . With combined \text { Lyman - } \alpha and Planck data , we find a slight ( 3 \sigma ) preference for negative running , \alpha _ { s } = -0.010 \pm 0.004 ( 68 % CL ) . Neutrino mass bounds are found to be robust against different assumptions . In the \Lambda \mathrm { CDM } model with running , we find \sum m _ { \nu } < 0.11 eV at the 95 % confidence level for combined \text { Lyman - } \alpha and Planck ( temperature and polarisation ) data , or \sum m _ { \nu } < 0.09 eV when adding CMB lensing and BAO data . We further provide strong and nearly model-independent bounds on the mass of thermal warm dark matter : m _ { X } > 10 \mathrm { keV } ( 95 % CL ) from \text { Lyman - } \alpha data alone .