The Monte Carlo simulation method was used to investigate ordering of particles interacting with the (12,6) Lennard-Jones potential and adsorbed on rectangular lattices. Systems consisting of particles of different sizes adsorbed on lattices characterized by different sizes of unit lattice cell were investigated. It is demonstrated that the ordered state of the adsorbed layer depends strongly on the relative sizes of adsorbed atoms and of the unit lattice cell of the solid surface lattice. Phase diagrams for several systems are determined and the critical behaviour of adsorbed layers is discussed. In particular, it is shown that despite the differences in the structure of the ordered state, all the systems considered here exhibit critical behaviour corresponding to the universality class of the two-dimensional Ising model.