This paper explores the production mechanism of the singlet vector lepton (VLL) and the Higgs self-interaction based on the theoretical and computational foundations related to the Higgs (Higgs) boson using the future positive-negative electronegative lepton collider (ILC). The discussion revolves around the discovery of VLLs and Higgs at the ILC and the significance of Higgs self-coupling strength for the Higgs potential. In the end, validation was achieved by conducting two sets of experimental tests. The VLL is being simulated to be found under the ILC collider in one set, and the Higgs coupling accuracy at the ILC collider is being tested in another set. The Higgs potential is dependent on the strength of the Higgs self-coupling, as demonstrated by the explorations and calculations. The light subchannel can be excluded from the mτ′± ∈ [180 GeV, 240GeV] integral luminosity when the ILC is

S=500GeV
\sqrt S = 500GeV

and the integral luminosity L ∈ [3.0fb−1,14.9fb−1]. For the e+ e− → HZZ-process, when n=3, mH = 115GeV,

s=3.5TeV
\sqrt s = 3.5{\rm{TeV}}

MS the upper limit is 5σ found in the unpolarized and +- polarization, where Pe+ = 0.6, Pe− = 0.8 it is able to reach 9.75 TeV and 10.1 TeV, respectively. Positively and negatively polarized linearly colliding beams can make a significant increase in the extra-dimensional effect of the e+ e− → HZZ-process. It is more efficient to exclude and find the monomorphic VLL and even Higgs through the full hadron channel of the LC.