There are two reasons for the asymmetry for the lipid composition of membranes in cells usually.
The first which was mentioned by @Superbest is proteins which are called 'flippases' which describes three broad categories of proteins which facilitate the translocation of the lipids through the membrane, despite the fact that they all have polar or even charged head groups.
This is not really an answer to your question here though - they will have little to do with asymmetry of lipids in erythrocytes I think because the these proteins will only allow lipid diffusion to equilibrium on either side of the membrane. To force an energetically unfavorable mixture of lipids they would require the use of energy. While some lipid translocases can force the composition to change against the equilibrium, these seem to require ATP and human erythrocytes do not have mitochondria.
The second, probably better answer is that the lipid composition of a membrane at equilibrium is dictated by of the curvature of the membrane. The outside of a membrane takes lipids with larger head groups and shorter or fewer chains, the interior will compose more of lipids with smaller head groups and longer and more aliphatic chains.
This capacity of a lipid to take up a greater volume in its head group vs its non-polar end is called its 'intrinsic curvature'.
Erythrocytes have some cytoskeletal structures such as ankyrins which give the cell its characteristic curvy 'dented lozenge' shape, which must also drive some of the lipid composition in some parts of the cell.