Your question is not clear. Is it about protein with high lysine content? If so, cation exchange chromatography seems the more appropriate as the high lysine content confers high pI and therefore these proteins are highly cationic at physiologial pH and will interact tightly with strong cation exchanger (MonoS sulfonic resin for instance).
Lysine is an aminoacid, so just a building block of a protein. You can separate Amino-acids using 2D electrophoresis as described here (1959): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1196994/?page=2
but I think it is an obsolete way of doing so, the best solution is by chromatography.
You need to give sufficient information for getting relevant answers, comments and suggestions. What is the size of your protein? Is your protein existing as a monomer, a dimer, trimer or oligomer under native conditions? SDS-PAGE is usually used for qualitative detection of proteins. You can use chromatographic techniques.