isoelectric point is when net charge is 0.
So lysine is a weak base. Lets go from fully protonated to fully deprotonated. (btw, this is TBR method that I liked a lot)
Fully protonated state has 2 protons with the nitrogens and one on the carboxylic acid. A net +2 charge due to the nitrogens. So pKa1 is losing the first proton, H3(2+) --> H2(+)
Now we lose the second proton. pKa2 is H2(+) --> (H). This! This is when there is no net charge. When pH = pKa2, then that is when the H2(+) = (H). So lets go a little higher till it's all (H). This is pKa2 + pKa3 / 2. This is the isoelectric point or one of the equivalence points in the titration graph.
Lose the last proton. pKa3 is no H and a net negative charge.