My assumptions: road bike, aero lever (cable routed under the handlebar tape), sidepull brake caliper.
Things to look at:
Simplest: WD40 the brake assembly around the bolt. Be careful not to get any on the tire or braking surface of the rim. Oil the cable, dripping onto the cable when the head sticks out of the lever. See if this frees things up.
More complex: loosen the bolt holding the brake in place to see if this frees up any movement. You may have to disassemble the caliper to clean and reassemble.
Hopefully one of the above will solve your problem.