The present note relies on the recently published conceptual design report of
the LHeC and extends the first contribution to the European strategy debate in
emphasising the role of the LHeC to complement and complete the high luminosity
LHC programme. The brief discussion therefore focuses on the importance of high
precision PDF and $alpha_s$ determinations for the physics beyond the Standard
Model (GUTs, SUSY, Higgs). Emphasis is also given to the importance of high
parton density phenomena in nuclei and their relevance to the heavy ion physics
programme at the LHC.
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