Abstract The heavy Higgs searches at LHC are carried out in gg→H→WW→lνlν, gg→H→ZZ→llll,llνν,llqq channels. The current searches for a heavy Higgs boson assume on-shell (stable) Higgs-boson production. The Higgs-boson production cross-section is then sampled with a Breit–Wigner distribution (with fixed-width or running-width) and implemented in Monte Carlo simulations. Therefore the question remains of what is the limitation of the narrow Higgs-width approximation. The main focus of this work is on the description of the Standard Model Higgs-boson lineshape in the heavy Higgs region, typically MH above 600 GeV. The framework discussed in this paper is general enough and can be used for all processes and for all kinematical regions. Numerical results are shown for the gluon-fusion process. Issues of gauge invariance and residual theoretical uncertainties are also discussed. Limitations due to a breakdown of the perturbative expansion are comprehensively discussed, including a discussion of the equivalence theorem for (off-shell) virtual vector-bosons. Analytic continuation in a theory with unstable particles is thoroughly discussed.