  We calculate the double-spin asymmetries $A_{\mathrm{LL}}$ for the processes
$\ell N\to h X$ and $\ell N\to {\mathrm{jet}}\, X$ at next-to-leading order
accuracy in perturbative QCD. We compare our theoretical results for
$A_{\mathrm{LL}}$ to data from the SLAC E155 experiment, finding only partially
satisfactory agreement. We conclude that measurements of $A_{\mathrm{LL}}$ and
the relevant polarized and unpolarized cross sections should be performed at
the present-day fixed-target lepton scattering experiments, as well as at a
future electron ion collider, in order to verify our understanding of this
process. We present predictions of the longitudinal double-spin asymmetries for
these experiments.
