<p>The neutron excess effect, originating from the vanishing of one part of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\varvec{\tau }}_\text {1} \cdot {\varvec{\tau }}_\text {2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">τ</mi> </mrow> <mtext>1</mtext> </msub> <mo>·</mo> <msub> <mrow> <mi mathvariant="bold-italic">τ</mi> </mrow> <mtext>2</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation> operator matrix elements, was appropriately considered within the Skyrme-type <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\Lambda N N\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Λ</mi> <mi>N</mi> <mi>N</mi> </mrow> </math></EquationSource> </InlineEquation> three-body interactions and applied to the deformed SHF model. Analysis of a broad range of hypernuclei, from light to heavy masses, shows that the neutron excess effect significantly improves the description of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\Lambda\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation> binding energies. The underlying mechanism involves reducing the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\Lambda N N\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Λ</mi> <mi>N</mi> <mi>N</mi> </mrow> </math></EquationSource> </InlineEquation> three-body repulsive interaction by subtracting the neutron excess term, thereby improving the binding energy of the hypernucleus. In addition, the impact of this effect on the <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\Lambda\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation> single-particle potential and the hyperon density distribution is discussed.</p>