Near-threshold varLambda {bar{varLambda }} mass spectra for the reactions e^+e^- rightarrow eta varLambda {bar{varLambda }} and e^+e^- rightarrow phi varLambda {bar{varLambda }} are investigated with an emphasis on the role played by the interaction in the varLambda {bar{varLambda }} system. A variety of varLambda {bar{varLambda }} potential models is employed that have been established in the analysis of data on p{bar{p}}rightarrow varLambda {bar{varLambda }} in the past. It is shown that the near-threshold enhancement observed for the two e^+e^- reactions can be reproduced by considering the varLambda {bar{varLambda }} final-state interaction in the partial waves suggested by the helicity-angle analysis of the experiments. For e^+e^- rightarrow eta varLambda {bar{varLambda }} the same varLambda {bar{varLambda }}S-wave interaction as in e^+e^- rightarrow varLambda {bar{varLambda }} is relevant and with it a consistent description of the pertinent measurements can be achieved. It is pointed out that a nonzero threshold cross section as observed for the latter reaction is not supported by the new eta varLambda {bar{varLambda }} data.