What is the charge of the amino acid lysine at pH 2?
At $\mathrm{pH}=2$, the charge will be: 

(charge near neutral pH, 2 groups positive, one negative) + (the fraction of the pKa = 2.18 group that is protonated)  

=1 + (the fraction of the $\mathrm{p}K_\mathrm{a} = 2.18$ group that is protonated) 

$=1 + 1/(1 + 10^{\mathrm{pH}-\mathrm{pK}}) =1 + 1/(1 + 10^{2-2.18})=1.60$ 

So the charge is +1.60, which is closer to 2 than 1, as you are saying.