Our Daisy sounds a lot like your Lucky. She is also very independent. She's a little bit different, though, in that when she first meets a strange dog, she goes berserk wanting to bowl them over and show them who's boss. However, after that first 30 seconds of acting crazy, she has very little interest in them. She basically acts like they aren't there. If they try to play with her, she just stands there and looks at them. The only time she will really react to another dog is if they try to put their leg over her neck or in some other way dominate her. Then she'll turn quickly with a growl toward them, they'll back off, and then Daisy will walk away in disgust throwing dirty looks at them. She doesn't fight, but she doesn't put up with those shenanigans, either.
We have done a little bit of fostering for Cavaliers, and this has held true whether we've had the fosters for 3 days or 8 weeks. Once the initial meet and greet silliness is over, Daisy just ignores them. Maybe she's just not met the "right" Cavalier, but so far, I would say that she is just not the type of dog to curl up next to another dog. It's funny because one of our fosters' adopters sent us an emailed picture of her other Cavalier and her new adoptee curled up asleep together on the couch looking very content about a week after they'd adopted him. We had had this guy in our house for 8 weeks and not once did Daisy and he ever sleep on the same piece of furniture together, ever. So I do think it's Daisy's standoffishness that prevents it. Obviously, that guy would have liked to cudddle if she'd been interested. Even when she was a puppy and we went to pick her up from the breeder, she tended to wander off a little from the others and entertain herself as you described.
So I guess the bottom line is do YOU want a second dog for you? If so, of course, go for it. But maybe don't go into it with high expectations of Lucky and the new guy being bosom buddies. That way if it happens, you'll be pleasantly surprised, but if it doesn't, you won't be disappointed.
The good part about Daisy's independence is that I don't feel too guilty when I leave her home alone when I'm at the office. And since my son was just diagnosed with allergies to dogs (among about 50 other things they tested him for), it looks like a 2nd dog is not in the forecast for us anyway (at least until he goes away to college!).