My thoughts:
Lost City: Card is obviously powerful, tricky thing is how bad the drawback is. I think that will actually vary pretty wildly, but it's pretty easy to underestimate. Obviously the card is best when that's not really a drawback - for instance, if they are drawing their deck anyways, or if they don't have enough buys to make all their money, or best of all if you possess them. The card is a LOT worse than village or lab when you only need one of those two effects. I guess you try to get this as late as possible - definitely prefer other draw cards first until you are over-terminal-ed - but it's going to depend a lot on the board. I think I like it, though I think people will overrate it out of the gate.
Magpie, that is an interesting one. It's easy to look at it and see all upside... and that doesn't seem far off. Only way it can be bad is that other things have more impact. Not great in a treasureless deck, but in about any deck with them, seems real solid. Doesn't do anything SUPER special by itself, but I imagine you will usually want to pick one up. Maybe you pick up another sometimes, especially if there's like, no trashing, but I imagine you're going to feel kind of bad for losing value. Big thing to note is that the pile will probably run really fast really often.
Hero: Basically impossible to analyze without the other cards in the chain. Just want to note that to get all the way to the top of these, it's going to take a lot of shuffles, so if you're counting on that, you need to prepare accordingly.