The Kohler model K-11465 toilet is one of the standard types in the Kohler line. The handle is situated on the upper left side of the toilet tank, and a handle attached to it inside of the toilet tank controls the flush valve mechanism. This particular arrangement is in wide use throughout the toilet industry, and will be familiar to any do-it-yourself person.
Damaged Handle
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Check the handle and make sure it is not damaged in any way. The toilet tank cover must be removed to access the handle lever inside the tank. A broken, cracked or bent handle or handle lever sticks, and the only alternative is to replace it.
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Chain Adjustment
The handle lever is attached to the flapper by a metal or a plastic chain. Proper chain adjustment allows the handle to completely pull the flapper up during the flush cycle. If the chain is adjusted with too much slack, the flapper does not fully open the tank drain, and the handle sticks in an upright position. If there is too little slack in the chain, the flapper opens and closes quickly, not fully draining the tank into the bowl, while the handle is stuck in a lower position. Proper chain adjustment allows the flapper to open fully when the handle is depressed, which moves the inside handle lever two-thirds of the way up.
Loose Handle Nut
The handle nut is located inside of the tank and holds the handle onto the tank securely. A loose nut causes the handle to stick, and won't allow the toilet to refill properly. Most handle nuts are made of plastic and can be hand-tightened, but they are threaded on counterclockwise to tighten. If a wrench is needed to fully tighten the nut, only tighten the nut until it is firm. Over tightening will crack the nut and necessitate its replacement.
Bad Flapper
The flapper is the seal between the toilet tank and the drain at the bottom of the tank that discharges into the toilet bowl proper. When the flapper gets old, or it has not been installed correctly, it remains in the open position and causes the handle to stick. In many cases, it appears as if the handle is causing the problem because it is stuck in an upright position. Check the flapper function by flushing the toilet as you watch. Once flushed, the flapper should ease back into position and seal off the tank drain.