you have never seen or played against a very good lucas I take it?
first off, lucas does not have a poor recovery in anyway. he has one of the best recoveries in the game. he may get hit a couple times ill give you that but he ALWAYS recovers.
lucas' don't spam PK fire, bad ones do but good ones do not. its very punishable though.
just play it like any normal match up. just f-tilt more and you'll be good
Ripple is right, Lucas' recovery is amazing. They don't even use their up-b unless it's their only choice and they don't have any jumps left. They have a few ways of recovering: They can jump and then z-air to the edge (z-edge), at the peak of their jump they can perform a wavebounced down b to shoot them horizontally back toward the stage, and they even have another crazy d-air super jump that can help them recover from incredibly low.
I've played Dire, Ninjalink, and Nasty in the DK vs Lucas matchup and I can say that you should never really go for grabs unless you get obvious openings. Shield grabs are a no brainer, but if you can read their landings pivot grabs work. F-tilt works great like Ripple said bc it outranges everything they have except PK fire.
If you get caught in their d-air, you can SDI up if you are quick enough. If not, just be ready to tech the ground so that you don't get caught by the d-tilt lock into *insert choice of smash attack* Also, make sure that the cargo release chain grab is not banned at your respective tournament before you go ahead and be gay =P
