If hares moved faster and were thus harder for lynx to capture, which rate in the lotka-volterra predator-prey model would change?

The rate that would change would be the searching efficiency/attack rate. There are only two other rates in this model: the growth rate of prey, and the predator or consumer mortality rate.

The searching efficiency/attack rate is what indicates how effectively can a predator capture its prey whether in the searching process or actual capturing/attacking process.