Blarg! Wtf are lures even for?! There a stop right at my favorite brewpub, so I drop a lure right when I get there. What do I get? F-ing Rattatas and F-ing Pidgeys!!!
Unsubstantiated rumor here that I heard someone read on Facebook about a blog someone else read. So, yeah.
Lures will most often attract the type of Pokémon most common to the area the stop is located. The increase in the chance of attracting a rare or rare to that area comes from the overall increase in Pokémon at a lured stop. So, not a big increase in chance, usually. It's a quantity thing, not a quality thing.
The best chance to up the chance of catching a rare at a stop is to lure on a stop at least 1 km from any other stop. So says, the chance is even greater if that stop is outside of an area that normally would spawn the ever so common rats and pidgeons. Yes, it does seem that rats and pigeons do flock to cities, just like real life. So, find a stop out in the boonies, and make sure it's at least 1 km from any other stop.
Then thinking here is that the game is programmed to spawn Pokémon where they're "expected to be". Rats and pigeons in cities. Carp, goldfish and other water types near water, and so on. Also, the game tracks how many of a thing has spawned there before, and uses that as part of the formula to spawn at lures. You're going to get more of the same because that's what's there. Now, this theory is, and it's a bit of leap because we don't know how the game historizes data or uses that history, is that if you go to where not a lot of people have lured before, you'll be in a place with less historical data for the game to use, and that will increase the odds of getting a truly rare Pokémon because the generation of Pokémon will be more random.
The thing about that is, what is random? That's a whole nuther topic. Even if every part of the theory is correct, people have been trying to create true random for a long time.