Light alkali metals have usually been considered as simple metals due to their monovalency and high conductivity. In these metals ionic pseudopotentials are weak and the nearly free electron model (NFE) becomes quite accurate at normal conditions. However, very recent experiments have shown that at high pressures their electronic properties deviate radically from the NFE model and even become unexpected good superconductors. In this work we present ab initio calculations to analyze the deviation from simplicity in a lithium monolayer (ML) when pressure is applied. We have seen that as a result of the increasing nonlocal character of the atomic pseudopotential with increasing pressure, the surprising half filling tight bindinglike nesting observed in the Fermi line can explain the interesting complex behavior in a lithium ML, induced by its correlated structural, electronic, and even magnetic properties.