The custodial Two-Higgs-Doublet-Model with SU(2) gauge fields is studied on the
lattice. This model has the same global symmetry structure as the Standard Model
but the additional Higgs field enlarges the scalar spectrum and opens the
possibility for the occurrence of spontaneous symmetry breaking of the global
symmetries. Both the spectrum and the running of the gauge coupling of the
custodial 2HDM are studied on a line of constant Standard Model physics with
cutoff ranging from 300 to 600 GeV. The lower bounds of the realizable masses
for the additional BSM scalar states are found to be well bellow the W boson
mass. In fact, for the choice of quartic couplings in this work the estimated
lower mass for one of the BSM states is found to be about $\sim 0.2m_{W}$ and
independent of the cutoff.