To get the sinking lure after you catch and keep a Pike, Ordon Catfish, and Bass fish, go past the bridge to the left side. Near the water there should be a little brown patch in the shape of a circle. Step on it and face north and manually fish (no boat).
Be sure to not select that lure if you take the boat with the fishing hole keeper on board, or she'll confiscate it and toss it back in the same spot where you can catch it once more.