Latitude on the choice of initialisation is a shared feature between one-step extended state-space and multi-step methods. The paper focuses on lattice Boltzmann schemes, which can be interpreted as examples of both previous categories of numerical schemes. We propose a modified equation analysis of the initialisation schemes for lattice Boltzmann methods, determined by the choice of initial data. These modified equations provide guidelines to devise and analyze the initialisation in terms of order of consistency with respect to the target Cauchy problem and time smoothness of the numerical solution. In detail, the larger the number of matched terms between modified equations for initialisation and bulk methods, the smoother the obtained numerical solution. This is particularly manifest for numerical dissipation. Starting from the constraints to achieve time smoothness, which can quickly become prohibitive for they have to take the parasitic modes into consideration, we explain how the distinct lack of observability for certain lattice Boltzmann schemes—seen as dynamical systems on a commutative ring—can yield rather simple conditions and be easily studied as far as their initialisation is concerned. This comes from the reduced number of initialisation schemes at the fully discrete level. These theoretical results are successfully assessed on several lattice Boltzmann methods. •We study the initialization of general lattice Boltzmann methods introducing an ad hoc modified equation analysis.•We find the constraints to obtain consistent initialization schemes, preserving second-order for the overall method.•We finely describe initial boundary layers due to dissipation mismatches between bulk and initialization schemes.•We introduce the observability of a lattice Boltzmann scheme, characterizing those with easily-mastered initializations.•We test the introduced analytical tools and their effectiveness through several—very conclusive—numerical experiments.