Ab initio total energy calculations are used to simulate the assembling of equiatomic APb alloys (A = Li, Na, K) from A(4)Pb(4) free clusters in order to investigate the remarkable stability of tetrahedral Pb-4 units in some of these solid and liquid alloys. Starting from a greatly expanded array of eight Na4Pb4 clusters per unit cell, the NaPb solid alloy was assembled by shrinking the unit cell and allowing full atomic relaxation at each stage. The evolution of cluster properties as the clusters are drawn together into the solid was studied. Charged (Pb-4)(4-) tetrahedral units were found to dominate the structural and electronic properties, being very robust and quite insensitive to their alkali environment. Trends with the choice of alkali were also investigated, showing that the stability of the (Pb-4)(4-) units decreases as we progress from K to Li and leads to their absence in the LiPb alloy in accordance with experiment. The critical factor for the survival of the units proved to be the distance between them, which was determined by the atomic size of the alkali. The effect of pressure on the systems was also considered.