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Infrared and nebular lines provide some of our best probes of the physicsregulating the properties of the interstellar medium (ISM) at high-redshift.However, interpreting the physical conditions of high-redshift galaxiesdirectly from emission lines remains complicated due to inhomogeneities intemperature, density, metallicity, ionisation parameter, and spectral hardness.We present a new suite of cosmological, radiation-hydrodynamics simulations,each centred on a massive Lyman-break galaxy that resolves such properties inan inhomogeneous ISM. Many of the simulated systems exhibit transient but welldefined gaseous disks that appear as velocity gradients in [CII]~158.6$\mu$memission. Spatial and spectral offsets between [CII]~158.6$\mu$m and[OIII]~88.33$\mu$m are common, but not ubiquitous, as each line probes adifferent phase of the ISM. These systems fall on the local [CII]-SFR relation,consistent with newer observations that question previously observed[CII]~158.6$\mu$m deficits. Our galaxies are consistent with the nebular lineproperties of observed $z\sim2-3$ galaxies and reproduce offsets on the BPT andmass-excitation diagrams compared to local galaxies due to higher starformation rate (SFR), excitation, and specific-SFR, as well as harder spectrafrom young, metal-poor binaries. We predict that local calibrations betweenH$\alpha$ and [OII]~3727$\AA$ luminosity and galaxy SFR apply up to $z>10$, asdo the local relations between certain strong line diagnostics (R23 and[OIII]~5007$\AA$/H$\beta$) and galaxy metallicity. Our new simulations are wellsuited to interpret the observations of line emission from current (ALMA andHST) and upcoming facilities (JWST and ngVLA).

Probing Cosmic Dawn with Emission Lines: Predicting Infrared and Nebular Line Emission for ALMA and JWST