  The recent report of near-ambient superconductivity in nitrogen-doped
lutetium hydrides (Lu-N-H) has generated a great interest. However, conflicting
results have raised doubts regarding superconductivity. Here, we combine
high-throughput crystal structure predictions with a fast predictor of the
superconducting critical temperature ($T_c$) to shed light on the properties of
Lu-N-H at 1 GPa. None of the predicted structures shows the potential to
support high-temperature superconductivity and the inclusion of nitrogen favors
the appearance of insulating phases. Despite the lack of near-ambient
superconductivity, we consider alternative metastable templates and study their
$T_c$ and dynamical stability including quantum anharmonic effects. The cubic
Lu$_4$H$_{11}$N exhibits a high $T_c$ of 100 K at 20 GPa, a large increase
compared to 30 K obtained in its parent LuH$_3$. Interestingly, it has a
similar X-ray pattern to the experimentally observed one. The LaH$_{10}$-like
LuH$_{10}$ and CaH$_6$-like LuH$_6$ become high-temperature superconductors at
175 GPa and 100 GPa, with $T_c$ of 286 K and 246 K, respectively. Our findings
suggest that high-temperature superconductivity is not possible in stable
phases at near-ambient pressure, but metastable high-$T_c$ templates exist at
moderate and high pressures.
