We study Λ and Λ¯ production asymmetries in pp¯→Λ(Λ¯)X, pp¯→J/ψΛ(Λ¯)X, and pp¯→μ±Λ(Λ¯)X events recorded by the D0 detector at the Fermilab Tevatron collider at s√=1.96  TeV. We find an excess of Λ’s (Λ¯’s) produced in the proton (antiproton) direction. This forward-backward asymmetry is measured as a function of rapidity. We confirm that the Λ¯/Λ production ratio, measured by several experiments with various targets and a wide range of energies, is a universal function of “rapidity loss,” i.e., the rapidity difference of the beam proton and the lambda.