Irony is when something unexpected happens, or the opposite of what you expect happens.
Candy partnering with George and Lennie is ironic because Candy’s relationship with his dog is like George and Lennie’s. Candy knows that when he is too old he will be replaced, as his dog was put out of its misery. At the end of the story, George puts Lennie out of his misery.
There are many connections between Candy and the puppies and Lennie. Lennie is often accidentally killing things because he wants to stroke them when they are soft. Candy’s old dog is shot, and they suggest he take one of the puppies. Lennie accidentally kills one of the puppies, just as he accidentally kills Curley’s wife.