I bought this and the Live kit at the same time, but for a couple of days I had it without Live. I was quite disappointed with the 1 player game, but by no means was it terrible. I trundled through the first chapter or so, and then....Live was working :)
Slightly tainted by my experiences with the one player game, I was still excited as hell. And once you've played this on Live, you may never sleep again. I haven't played the 1 player game since, the live experience is incredibly fufilling. I don't talk on it much, the Americans and French people intimidate me :P but since every game is completely different it really is great. It also seems that the developers are actively involved with it after release 2, with 3 new levels being offered through Content Download. 2 of which are really good (and for some reason no-one ever plays Barn).
You're never without a game to play, and you can of course start your own game, and try get a place on the hosting leaderboard. Even behind a router with 4 PCs on it I could comfortably host a 6 player game.
Lag is enevitable, and is really a fault of the players, not the game. It only takes one person to join the game with an extremely slow connection being shared with another million computers, behind a firewall and 18 routers to destroy the game for everyone, but they do get disconnected after a wee while if they're causing it. I feel sorry for those who can never get in a game - after all they splashed out on all this stuff for nothing, but maybe they should 'optimise' their connection. Lag isn't that bad, perhaps 1 in 10 games is laggy.