The distribution of (elastic) lattice strains following plastic deformation of an aluminium alloy is examined using finite element simulations of aggregates with individually resolved crystals. The aggregates consist of face centred cubic crystals with initial orientations assigned by sampling the measured crystallographic texture. The simulations show that the lattice strains within the crystals are influenced by various microstructural features, material parameters and modelling assumptions. A hierarchy among these various effects is established, based on applications where low probability events are crucial, such as in fatigue or fracture problems. The simulation results are discussed in detail and compared with experimental data for the macroscopic stress, the lattice strains in the unloaded state and the associated uncertainties.