For hemoglobin electrophoresis usually is apply a detergent-based lysis, e.g. saponin 1%.
For HPLC is important to note recommendations of the manufacturer, for variant system from BioRad, total blood or blood diluted in distilled water can be used.
Distilled water is the commonly used lysing agent for the older/mid-range HPLCs. For the recent ones like BIO-RAD VARIANT II, it's all automatic. You just have to place the EDTA sample in the rack and lysis will be done automatically after the sample has been aspirated.
Triton X-100, 0.5 ml in 100 ml of 100 mg/L KCN solution is mentioned in recent edition of Practical Haematology by Dacie & Lewis as a lytic agent for hemoglobin electrophoresis on cellulose acetate membrane. HPLC needs to use the lytic agent supplied by the manufacturer.