  Upcoming large galaxy surveys will subject the standard cosmological model,
$\Lambda$CDM, to new precision tests. These can be tightened considerably if
theoretical models of galaxy formation are available that can predict galaxy
clustering and galaxy-galaxy lensing on the full range of measurable scales
throughout volumes as large as those of the surveys and with sufficient
flexibility that uncertain aspects of the underlying astrophysics can be
marginalised over. This, in particular, requires mock galaxy catalogues in
large cosmological volumes that can be directly compared to observation, and
can be optimised empirically by Monte Carlo Markov Chains or other similar
schemes to eliminate or estimate astrophysical parameters related to galaxy
formation when constraining cosmology. Semi-analytic galaxy formation methods
implemented on top of cosmological dark matter simulations offer a
computationally efficient approach to construct physically based and flexibly
parametrised galaxy formation models, and as such they are more potent than
still faster, but purely empirical models. Here we introduce an updated
methodology for the semi-analytic L-GALAXIES code, allowing it to be applied to
simulations of the new MillenniumTNG project, producing galaxies directly on
fully continuous past lightcones, potentially over the full sky, out to high
redshift, and for all galaxies more massive than $\sim 10^8\,{\rm M}_\odot$. We
investigate the numerical convergence of the resulting predictions, and study
the projected galaxy clustering signals of different samples. The new
methodology can be viewed as an important step towards more faithful
forward-modelling of observational data, helping to reduce systematic
distortions in the comparison of theory to observations.
