Michaelis–Menten second-order chemical kinetics is used to describe the three main mechanisms for surviving fractions of cells after irradiation. These are a direct yield of lethal lesions by single event inactivation, metabolic repair of radiation lesions and transformation of sublethal to lethal lesions by further irradiations. The mass action law gives a system of time-dependent differential equations for molar concentrations of the invoked species that are the DNA substrates as lesions, enzyme repair molecules, the product substances, etc. The approximate solutions of these coupled rate equations are reduced to the problem of finding all the roots of the typical transcendental equation \(ax\mathrm{e}^{-bx}=c\) with \(x\ge 0\) being a real variable, where \(a,b\) and \(c\) are real constants. In the present context, the unique solution of this latter equation is given by \(x=(1/b)W_0(bc/a)\) where \(W_0\) is the principal-branch real-valued Lambert function. Employing the concept of Michaelis–Menten enzyme catalysis, a new radiobiological formalism is proposed and called the “Integrated Michaelis–Menten” (IMM) model. It has three dose-range independent parameters ingrained in a system of the rate equations that are set up and solved by extracting the concentration of lethal lesions whose time development is governed by the said three mechanisms. The indefinite integral of the reaction rate is given by the Lambert \(W_0\) function. This result is proportional to the sought concentration of lethal lesions. Such a finding combined with the assumed Poisson distribution of lesions yields the cell surviving fraction after irradiation. Exploiting the known asymptotes of the Lambert \(W_0\) function, the novel dose-effect curve is found to exhibit a shoulder at intermediate doses preceded by the exponential cell kill with a non-zero initial slope and followed by the exponential decline with the reciprocal of the \(D_0\) or \(D_{37}\) dose as the final slope. All three dose regions are universally as well as smoothly covered by the Lambert function and, hence, by the ensuing cell surviving fractions. The outlined features of the proposed IMM model stem from a comprehensive mechanistic description of radiation-lesion interactions by means of kinetic rate equations. They are expected to be of critical importance in new dose-planning systems for high doses per fraction where the conventional linear-quadratic radiobiological modeling is demonstrably inapplicable.