<p>The goal of this paper is to present new results on generalized polynomial sequence known as degenerate Lévy-Meixner Appell polynomials <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1721_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="141" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {P}_{\lambda }=\{P_{n, \lambda }, n\in \mathbb {N}\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="double-struck">P</mi> <mi>λ</mi> </msub> <mo>=</mo> <mrow> <mo stretchy="false">{</mo> <msub> <mi>P</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>λ</mi> </mrow> </msub> <mo>,</mo> <mi>n</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> <mo stretchy="false">}</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> associated with the infinite-dimensional degenerate Lévy-Meixner distribution. Additionally, the connection that exists between brand-new polynomials, the degenerate falling operators and the Bell polynomials has been investigated. This paper presents novel properties of the kernels <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1721_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\(P_{n, \lambda }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>λ</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> in infinite dimensions, offering valuable insights, broadening the scope of our results.</p>