Physiological pH is between 7.37 and 7.43
Lysine is a basic amino acid, which means it has two NH2 groups and one COOH group.
Lysine pKas are: 2.16, 9.06 and 10.05
At low pH (lower than the first pKa, in this case: lower than 2.16) the three groups are protoned. As you increase pH, the first group to lose its proton is the acid group, then the alpha-amino group and then the R-amino group. You will have everything non protoned at a high pH (higher than the highest pKa, in this case: 10.05).
Physiological pH is higher than the lowest pKa and lower than the middle pKa, so it’s the second case: the acid is not protoned, the R-amino is protoned and the alpha amino is protoned.
Protoned aminos are cations: NH3+.