The nuclear-charge expansion method is used to calculate multiplet strengths, correct through first order, for 1s²nl²L-1s²ml'²L' dipole transitions in lithium-like ions for all n,m<or=4. Two distinct procedures, which give results in very close agreement, are used and a modified screening approximation is employed to increase the rate of convergence of the expansions. From these calculated values and experimental energy differences, oscillator strengths and radiative lifetimes for a range of atomic ions are predicted and compared with other available data.