The aim of this paper is to study the limiting behaviour of lattice filters with a fixed number of stages as the sampling period tends to zero. Under this constraint, the conditional lattice filters are shown either to have no limits, or such limits can only realize continuous-time transfer functions with every other order. The authors propose to modify the conventional lattices in order to obtain new lattice structures that have an order-recursive continuous-time limit that can realize any arbitrary all-pole transfer function. Time-invariant and time-varying stability of these filters is investigated in detail for both the discrete-time and the limiting continuous-time structures. Numerical results illustrate the improvement of the modified normalized lattice filter over the conventional normalized lattice filter for very small sampling periods and finite precision implementation.