  The missing mass spectrum measured in high resolution studies of the reaction
pp -> K^+X is analyzed with respect to the strong final state interaction near
the Lambda p production threshold. The observed spectrum can be described by
factorizing the reaction amplitude in terms of a production amplitude and a
final state scattering amplitude. Parametrizing the Lambda p final state
interaction in terms of the inverse Jost function allows a direct extraction of
the low-energy phase-equivalent potential parameters. Constraints on the
singlet and triplet scattering lengths and effective ranges are deduced in a
simultaneous fit of the Lambda p invariant mass spectrum and the total cross
section data of the free Lambda p scattering using the effective range
approximation.
