Background:In π + n and π − p electroproduction, conventional models cannot satisfactorily explain the data above the resonance region, in particular the transverse cross section. Although no high-energy L-T-separated cross-section data are available to date, a similar scenario can be inferred for K + Λ electroproduction. Purpose: Develop a phenomenological model for the p(γ * ,K + )Λ reaction at forward angles and high-energies. Propose a universal framework for interpreting charged-kaon and charged-pion electroproduction above the resonance region. Method: Guided by the recent model for charged-pion electroproduction, developed by the authors, a framework for K + Λ electroproduction at high energies and forward angles is constructed. To this end, a Reggeized background model for K + Λ photoproduction is first developed. This model is used as a starting base to set up an electroproduction framework. Results: The few available data of the unseparated p(γ * ,K + )Λ cross section are well explained by the model. Predictions for the L-T-separation experiment planned with the 12 GeV upgrade at Jefferson Lab are given. The newly proposed framework predicts an increased magnitude for the transverse structure function, similar to the situation in charged-pion electroproduction. Conclusions: Within a hadronic framework featuring Reggeized background amplitudes, s-channel resonanceparton effects can explain the observed magnitude of the unseparated p(γ * ,K + )Λ cross section at high energies and forward angles. Thereby, no hardening of the kaon electromagnetic form factor is required.