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Let p be an odd prime and let ρ : ℤ / p → GL n ⁡ (ℤ) be an action of ℤ / p on a lattice and let Γ := ℤ n ⋊ ρ ℤ / p be the corresponding semidirect product. The torus bundle M := T ρ n × ℤ / p S ℓ over the lens space S ℓ / ℤ / p has fundamental group Γ. When ℤ / p fixes only the origin of ℤ n , Davis and Lück (2021) compute the L-groups L m 〈 j 〉 ⁢ (ℤ ⁢ [ Γ ]) and the structure set 풮 geo , s ⁢ (M) . In this paper, we extend these computations to all actions of ℤ / p on ℤ n . In particular, we compute L m 〈 j 〉 ⁢ (ℤ ⁢ [ Γ ]) and 풮 geo , s ⁢ (M) in a case where E ¯ ⁢ Γ has a non-discrete singular set. [ABSTRACT FROM AUTHOR]