The Large Hadron-electron Collider (LHeC) is a proposed upgrade of the Large Hadron Collider (LHC). An energy recovery linac would provide 60 GeV electrons to collide with the proton and nuclear beams from the High Luminosity LHC (HL-LHC) and, eventually, with those from the High Energy LHC (HE-LHC) and the Future Circular Collider in hadron-hadron mode (FCC-hh). Working concurrently with the pPb or PbPb LHC modes, it will provide ePb collisions in the TeV regime with luminosities $\sim 10^{33}$ cm$^{-2}$s$^{-1}$ to achieve integrated luminosities $\sim 10$ fb$^{-1}$ in ten years. It will offer a huge extension of the kinematical coverage with respect to the one presently covered by data used in nuclear parton density functions (nPDF) fits, down to $x\sim 10^{-6}$ in the perturbative region for the LHeC. In this contribution I will show the possibilities in such machine for determining the nPDFs with unprecedented precision, in a region of interest for both HL-LHC and future AA colliders, with the possibility of extracting the complete set of PDFs of a single nucleus in a single experiment. Confronting such precision nPDFs with data from nuclear colliders will then set the eventual factorisation breaking effects and allow a more precise characterisation of the properties of the Quantum Chromodynamics (QCD) matter produced in such collisions. I will also comment on the possibilities for the extraction of diffractive parton densities in proton and nucleus.