Novel data from the $K^{-}_{stop}A$ absorption reaction in light nuclei $^{6,7}$Li and $^{9}$Be are presented. The study aimed at finding $Lambda t$ correlations. Regardless of $A$, the $Lambda t$ pairs are preferentially emitted in opposite directions. Reaction modeling predominantly assigns to the $K^-_{stop}AtoLambda t(N)A$ direct reactions the emission of the $Lambda t$ pairs whose yield is found to range from $10^{-3}$ to $10^{-4}$$/K^-_{stop}$. The experiment was performed with the FINUDA spectrometer at DA$Phi$NE (LNF).