This paper proposes an adaptive lattice-based motion planning solution to address the problem of generating feasible trajectories for systems, represented by a linearly parameterizable non-linear model operating within a cluttered environment. The system model is considered to have uncertain model parameters. The key idea here is to utilize input/output data online to update the model set containing the uncertain system parameter, as well as a dynamic estimated parameter of the model, so that the associated model estimation error reduces over time. This in turn improves the quality of the motion primitives generated by the lattice-based motion planner using a nominal estimated model selected on the basis of suitable criteria. The motion primitives are also equipped with tubes to account for the model mismatch between the nominal estimated model and the true system model, to guarantee collision-free overall motion. The tubes are of uniform size, which is directly proportional to the size of the model set containing the uncertain system parameter. The adaptive learning module guarantees a reduction in the diameter of the model set as well as in the parameter estimation error between the dynamic estimated parameter and the true system parameter. This directly implies a reduction in the size of the implemented tubes and guarantees that the utilized motion primitives go arbitrarily close to the resolution-optimal motion primitives associated with the true model of the system, thus significantly improving the overall motion planning performance over time. The efficiency of the motion planner is demonstrated by a suitable simulation example that considers a drone model represented by Euler-Lagrange dynamics containing uncertain parameters and operating within a cluttered environment.