We describe our non-linear emulation (i.e. interpolation) framework that combines the halo occupation distribution (HOD) galaxy bias model with N-body simulations of non-linear structure formation, designed to accurately predict the projected clustering and galaxy-galaxy lensing signals from luminous red galaxies in the redshift range 0.16 < z < 0.36 on comoving scales 0.6 < rp < 30 h^{-1} Mpc. The interpolation accuracy is ≲ 1-2 per cent across the entire physically plausible range of parameters for all scales considered. We correctly recover the true value of the cosmological parameter S8 = (σ8/0.8228)(Ωm/0.3107)0.6 from mock measurements produced via subhalo abundance matching (SHAM)-based light-cones designed to approximately match the properties of the SDSS LOWZ galaxy sample. Applying our model to Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 14 (DR14) LOWZ galaxy clustering and galaxy-shear cross-correlation measurements made with Sloan Digital Sky Survey (SDSS) Data Release 8 (DR8) imaging, we perform a prototype cosmological analysis marginalizing over wCDM cosmological parameters and galaxy HOD parameters. We obtain a 4.4 per cent measurement of S8 = 0.847 ± 0.037, in 3.5σ tension with the Planck cosmological results of 1.00 ± 0.02. We discuss the possibility of underestimated systematic uncertainties or astrophysical effects that could explain this discrepancy.