I'm seriously impressed with the range of reaching in this thread!
From vague details from the OP, we've got complaints that the cycle maintenance knowledge doesn't add up, "it's an affair" stated as absolute fact, questioning why two outdoorsy people wanted to make the best of a broken bike, and people who don't want to accept that others can be friends without banging, illustrated through a series of illogical questions. "But why didn't he..."
If you read and twist everything the OP says as uncharitably as possible, then it doesn't sound good. But who does that to someone they love and have spent 18 years with? That's fairly unpleasant behaviour. There's no actual proof whatsoever that he's told a single lie. In fact, it's his own words that are being thrown back in his face!
Sorry if you've had a bad experience or been cheated on, but your happiness is your own responsibility. She knew he was going out for the day, but chose to make no alternate plans whatsoever. Doesn't even have the gumption to book a trip out. Sits at home sulking. If I'd come home from a bike ride to that, it would take the shine off my hobby completely, and frankly, make me think less of my partner.
Unless there's any proof whatsoever that he lied, I don't see that there's a leg to stand on, other than letting him enjoy his hobby.