It took me a long while to get used to Dtilt as well. Frame 2-3 move with a better pushback at the end of the move and a weird horiztonal angle as opposed to an anti-air, free kill setup / major hitstun 'lock.' It's pretty balanced, just weird.
tl;dr use to cover gaps in pressure. Dtilt is a nice move that sets up for chase downs and can shift momentum into your favor. Very useful when properly applied, much better to use in neutral than old 3.02 Dtilt.
I find it's a relatively safe option to cover holes in Lucas' pressure and keeps him grounded. Nair -> Dtilt can do wonders against even the best crouch cancels: Yoshi, Bowser, DK, etc.
The slight knockback setups up well for Fair combo strings (Fair into Fair into Fair or Fair into Uair, etc). You get the picture.
If they're at low % and barely go anywhere, use a Nair to followup as they can buffer pulling up shield or will fast fall -> CC the next move and counter attack. Nair will either be a safe hit on shield or beat the crouch cancel. You may also opt to use a retreating DJC PKF of the enemy has already landed and is about to use a CC counterattack
At mid% you might start getting more Sweetspot Fairs if you immediately run right after they get knocked back from Dtilt.
At 50-60% or higher, Dtilt -> chase down with an approach DJC PKF and force their options. Most attacks won't followup from Dtilt when they're at this %.