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Upcoming large galaxy surveys will subject the standard cosmological model,$\Lambda$CDM, to new precision tests. These can be tightened considerably iftheoretical models of galaxy formation are available that can predict galaxyclustering and galaxy-galaxy lensing on the full range of measurable scalesthroughout volumes as large as those of the surveys and with sufficientflexibility that uncertain aspects of the underlying astrophysics can bemarginalised over. This, in particular, requires mock galaxy catalogues inlarge cosmological volumes that can be directly compared to observation, andcan be optimised empirically by Monte Carlo Markov Chains or other similarschemes to eliminate or estimate astrophysical parameters related to galaxyformation when constraining cosmology. Semi-analytic galaxy formation methodsimplemented on top of cosmological dark matter simulations offer acomputationally efficient approach to construct physically based and flexiblyparametrised galaxy formation models, and as such they are more potent thanstill faster, but purely empirical models. Here we introduce an updatedmethodology for the semi-analytic L-GALAXIES code, allowing it to be applied tosimulations of the new MillenniumTNG project, producing galaxies directly onfully continuous past lightcones, potentially over the full sky, out to highredshift, and for all galaxies more massive than $\sim 10^8\,{\rm M}_\odot$. Weinvestigate the numerical convergence of the resulting predictions, and studythe projected galaxy clustering signals of different samples. The newmethodology can be viewed as an important step towards more faithfulforward-modelling of observational data, helping to reduce systematicdistortions in the comparison of theory to observations.

The MillenniumTNG Project: Semi-analytic galaxy formation models on the past lightcone