  Here we study the effect of La doping in EuO thin films using SQUID
magnetometry, muon spin rotation ($\mu$SR), polarized neutron reflectivity
(PNR), and density functional theory (DFT). The $\mu$SR data shows that the
La$_{0.15}$Eu$_{0.85}$O is homogeneously magnetically ordered up to its
elevated $T_{\rm C}$. It is concluded that bound magnetic polaron behavior does
not explain the increase in $T_{\rm C}$ and an RKKY-like interaction is
consistent with the $\mu$SR data. The estimation of the magnetic moment by DFT
simulations concurs with the results obtained by PNR, showing a reduction of
the magnetic moment per La$_{x}$Eu$_{1-x}$O for increasing lanthanum doping.
This reduction of the magnetic moment is explained by the reduction of the
number of Eu-4$f$ electrons present in all the magnetic interactions in EuO
films. Finally, we show that an upwards shift of the Fermi energy with La or Gd
doping gives rise to half-metallicity for doping levels as high as 3.2 %.
