DOS pointed you in he right direction. The lever doesn't have a return spring (with a few exceptions) so it depends on the spring in the caliper for return action. So, working backwards, it's either a weak spring in the caliper, friction or binding in the caliper, friction in the cable, or friction in the pivots of the lever itself.
You can isolate the problem, by squeezing the caliper and letting go, then squeezing the caliper to slacken the cable and sliding the housing up and down within the slack, or working the lever alone with a slack cable.
My bet on an older used bike is simple cable friction. Squeeze the caliper to get some slack, and apply a thin oil like Tri-flow, or light household oil (do they still sell sewing machine oil?) and let it wick in. Also use The same on the brake caliper pivots, and blot off the excess so it doesn't attract dust.
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FB
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