okay well. the way I see it we still need to discuss this matchup, so i'll give it a fair shake.
Approaching DK: This.. is difficult. imagine marth, he shuts down most of our approaches using a combination of dsmash, dair, and uair. DK can absolutely wreck you if you do not autocancel every single one of your moves perfectly, and even if you do cancel them perfectly, a grab can put you in a bad place quick, so, dont autocancel ANY move in front of DK, if the DK is shielding it will end badly. Use PKF alot. DK can swat away projectiles with ftilt, but PKF can still be useful if you use it the right way.
Oh. And dont grab. seriously. grabbing a DK is difficult, ape can outspace us in most regards and the ropesnake does little to help here.
Damaging DK: Most moves here are risky to use, other then the usual, some stuff to keep in mind is that:
A. DK has very little cover from below himself
B. DK is difficult to approach from any other place
Luckily, due to his weight and difficulty attacking opponents below him in the air, you can chain uairs on DK until a relatively low percentage. nair is also a good move. the longer you keep DK in the air, the better off you are, but keep in mind that bair and uair are both incredible aerials, and fair can easily knock you down a peg.
fighting DK has always been a spacing game. and unfortunately, DK completely destroys lucas in this regard, so even discounting the really bad things about the matchup, it still isn't very pretty for lucas.
If you get grabbed at above 100%, kiss your stock goodbye. cargo release to Dsmash time.
As far as stages are concerned, ban jungle japes. seriously, DK is almost as difficult to beat there as falco is, and will survive until ludicrous percentages due to the horizontal nature of his up B. as far as stage to CP DK on... I really dont know. Almost every stage where lucas is good DK is at a distinct advantage on.
I guess either frigate or delfino. RC if you're comfortable there, which I doubt.
65:35 without the infinite, unwinnable matchup with it