Cross-section distributions are calculated for the reaction e(+)e(-) -> J/psi -> (Lambda) over bar(-> (p) over bar pi(+)) Lambda(-> p pi(-)), and related annihilation reactions mediated by vector mesons. The hyperon-decay distributions depend on a number of structure functions that are bilinear in the, possibly complex, psionic form factors G(M)(psi) and G(E)(psi) of the Lambda hyperon. The relative size and relative phase of these form factors can be uniquely determined from the unpolarized joint-decay distributions of the Lambda and anti-Lambda hyperons. Also the decay-asymmetry parameters of Lambda and anti-Lambda hyperons can be determined.