If your lawn mower's throttle cable is hard to move or stuck, here's a fix. Disconnect both ends of the cable from the mower. You'll probably have to remove a bolt and disassemble the lever assembly near the handle to get the cable out. Take a digital photo to help you put it back together when you're done.
At the engine end, loosen the clamp that holds the cable to the engine and unhook the cable from the carburetor. Pour penetrating oil into the cable (Photo 1). Grab the inner cable with pliers and work it up and down to loosen it. When the cable moves freely and all the penetrating oil has drained out, squirt silicone lubricant into the funnel to keep the cable sliding freely. Reinstall the cable (Photo 2).