The problem of estimating the relative probability P of recoilless Lambda -production in nuclei by means of the (K^-, pi ^-) reaction is investigated in the plane-wave impulse approximation. It is shown on the basis of this and certain other approximations that P may be given by a very simple expression, namely by a Gaussian of the momentum transfer q, in which the harmonic oscillator quantum number of the outer shell and the oscillator spacings and (reduced) masses of the Lambda and the nucleon appear. The overlap integrals between the Lambda and the nucleon wavefunctions are found to be close to unity and can usually be omitted in the expression for P. Numerical estimates of P are also made for a number of hypernuclei.