Let G be a simply-connected (real) Lie group. A lattice Γ in G is said to be rigid if every automorphism of Γ extends to an automorphism of G. Landmark results in the context of semisimple groups are the Mostow Rigidity Theorem and the Margulis Superrigidity Theorem. In this talk I will report on onging joint work with Oliver Baues, concerning rigidity and non-rigidity of lattices in soluble Lie groups. I will start by discussing a classical theorem of Maltśev–Saitô, instructive examples given by Starkov and a result of Witte. Then I will explain our more recent approach towards a ‘quantative description’ of the phenomenon of non-rigid lattices in soluble Lie groups.