  We implement a model for the two-point statistics of biased tracers that
combines dark matter dynamics from $N$-body simulations with an analytic
Lagrangian bias expansion. Using Aemulus, a suite of $N$-body simulations built
for emulation of cosmological observables, we emulate the cosmology dependence
of these nonlinear spectra from redshifts $z = 0$ to $z=2$. We quantify the
accuracy of our emulation procedure, which is sub-per cent at $k=1\, h {\rm
Mpc}^{-1}$ for the redshifts probed by upcoming surveys and improves at higher
redshifts. We demonstrate its ability to describe the statistics of complex
tracer samples, including those with assembly bias and baryonic effects,
reliably fitting the clustering and lensing statistics of such samples at
redshift $z\simeq 0.4$ to scales of $k_{\rm max} \approx 0.6\,
h\mathrm{Mpc}^{-1}$. We show that the emulator can be used for unbiased
cosmological parameter inference in simulated joint clustering and
galaxy--galaxy lensing analyses with data drawn from an independent $N$-body
simulation. These results indicate that our emulator is a promising tool that
can be readily applied to the analysis of current and upcoming datasets from
galaxy surveys.
