Bad toilet cut-off lever ? ? ?

Problem with Kohler single-unit toilet:
The cut-off lever at the top of the flushing mechanism sticks. The float doesn't force it up even when the float is completely covered with water. I have to lift the lever with my finger.
I can't seem to get the blue cap off to make an adjustment.
I tried spraying WD-40 on the lever, and it didn't help.
Then I tried liquid dish detergent to make it slippery. That seemed to help for a while, but it had the unfortunate side effect of dissolving the rubber flush flap.
Here is a website which shows a photo of the problem:
Any help most welcome:

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