Let L be a J -subspace lattice on Banach space X and AlgL be the associated J - subspace lattice algebra. A ternary derivation on AlgL is defined as a triple of linear mappings (γ, δ, τ) : AlgL → AlgL that satisfies the condition γ (AB) = δ(A)B + Aτ(B) for all A, B ∈ AlgL. We establish that for given linear maps δ, τ on AlgL, there exists a unique linear map γ on AlgL defined by γ (A) = R A + AS for some R, S ∈ L(X) such that (γ, δ, τ) forms a ternary derivation on AlgL if and only if δ, τ satisfy δ(A)B + Aτ(B) = 0 for any A, B ∈ AlgL with AB = 0. As applications of this result, we provide a comprehensive characterization of linear mappings δ and τ. Additionally, we investigate linear mappings that are derivable at zero, (left/right) centralizers, (left/right) ideal-preserving mappings, and local (generalized) derivations within JSL algebras. These findings are applicable to atomic Boole
