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This paper is a continuation of the author's previous work, where we studiedthe variation of the number of isomorphic classes of $G_{\mathbb{Q}}$-stablelattices in p-adic families of residually reducible ordinary Galoisrepresentations. In this paper, we study the number of isomorphic classes of$G_{\mathbb{Q}}$-stable free lattices in a residually reducible Hidadeformation and the variation of their related two-variable algebraic $p$-adic$L$-functions. This result gives an answer of a question asked by Ochiai.

Stable $\mathbb{I}$-free lattices and the two-variable algebraic $p$-adic $L$-functions in residually reducible Hida deformation