This work provides the first combined analysis of low-energy pΛ scattering, considering both cross section and correlation data. The obtained results establish the most stringent constraints to date on the two-body pΛ interaction, pointing to a weaker attraction than so far accepted. The best set of scattering lengths for the spin singlet and triplet are found to range from <math><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mo>(</mo><mn>2.1</mn><mo>,</mo><mn>1.56</mn><mo>)</mo></math> to <math><mo>(</mo><mn>3.34</mn><mo>,</mo><mn>1.18</mn><mo>)</mo></math> fm. With a chiral NY potential fine-tuned to those scattering parameters, the in-medium properties of the Λ are explored and a potential depth of <math><msub><mrow><mi>U</mi></mrow><mrow><mi>Λ</mi></mrow></msub><mo>=</mo><mo>−</mo><mn>36.3</mn><mo>±</mo><mn>1.3</mn><msubsup><mrow><mo>(</mo><mi>stat</mi><mo>)</mo></mrow><mrow><mo>−</mo><mn>6.2</mn></mrow><mrow><mo>+</mo><mn>2.5</mn></mrow></msubsup><mrow><mo>(</mo><mi>syst</mi><mo>)</mo></mrow></math> MeV is found at nuclear matter saturation density.