If your brakes are the same model and series and your levers the same model and series, then your issue is likely the pads are spaced further on one brake than the other. As
cxwrench said, just loosen the pinch bolt on the cable and you can squeeze them to where you need them then re-tighten the pinch bolt. You can also change that with the barrel adjust screw that might be on your brakes if it's not outside the limits of it. It'd be nice to know what brakes you have because a certain model of Shimano brakes also has a tension adjustment. Though probably not your issue.
As well, if someone was messing with the reach adjustment screw underneath the hood of the STI, it might make you think the lever travel is less in one than the other.
You don't need special tools to do what you are asking. Or is this thread just a tool show thread?