First off, have you checked out Vaginas Are Magic or Eldritch Cock? The PDFs are available for free and if you go with the magic system presented there, then that may give you a more viable way to bring in the DCC spells and systems.
Regarding the DC# stat checks, I think you can handle them a few different ways. The simplest, just either convert them in to saving throws or roll under stat rolls. DC 8 Fort Save becomes a save vs magic, DC 8 Intelligence becomes a "roll a d20 and roll equal to or less than your INT score" and DC 7 Reflex check could be a save against device, or a roll under DEX score.
This is typically how hazards are handled in LotFP anyway, so you're just ignoring the various levels of difficulty and making them into straight up saves.
Now, the slightly more complicated way would be you could cross check the DCs with LotFP saves and figure out where the sweet spot is - like is a DC 8 similar to having a save of 12? then just give a bonus or penalty to the saving throw when the DC is harder or easier than the "sweet spot." Personally, I'd just go with straight up saves and allow half saves on easier DCs.
(If you use the new saving throw system from VAM or EC, then it's even easier - it's either a magic or non-magic save, and you always allow a half save.)
Eldritch Cock also features the new playtest rules, which includes a mechanic for Luck. You could use that and replace the one in DCC, or you could use the DCC one and just have players record it on their character sheet and use the rule as-is.
(I use luck in my games, but it's a bit different from both - players take the average of all their stats, and that is their initial luck roll. They can burn points from it to reroll like in DCC, but only get 1 new luck point when leveling up. To make a luck save, they roll the die matching their luck number (so if it's 11, they roll a d11 or a d12 and reroll on a 12) and if they roll a 1, they fail. This creates a fun tension between wanting as high a luck value as possible, while also wanting to burn points to get rerolls.)