So what can Night Lords do against Death Guard?
Simple, negate what strengths or bonus's you can. Death Guard armies get 'stealth' at 18"+? Get to short range faster than they can escape it.
Your Night Lords, raptors are troops for you; so your required squads, if using a CAD, can deep strike and negate the Death Guard 'stealth.' Use warp talons, negating armour saves makes it harder for plague marines to survive.
Helldrakes are going to be your friend, due to their speed and the ability of baleflamers to ignore the armour of plague marines.
Death Guard get the mark of nurgle (so the good T5 marines, Oblits termies etc) - Night Lords don't.
Death Guard units that are not Typhus or plague marines also lower their initiative, unless I am mistaken here.
So a portion of their units will strike after your units in close combat, where you can do more damage with the likes of your HQ, raptors, chosen, terminators, and warp talons.
Add in re-rolls of FNP vs the ability to be swept in cc :/
Your playing a fast, elite army that can bring a lot of AP3 to bear in close combat. Your army has the ability to negate several of your enemies resilience buffs (the ranged shrouded and the natural resilience of power armour.)
Your opponent is a reslient, elite army that can take a lot of ranged punishment but is at a disadvantage in close combat. They are slower, have fewer attacks, and rely on a combination of power armour and feel no pain to negate the majority of the damage coming their way.
So what can/should you do? Focus on the Night Lord strengths that are applicable in this situation. That means Close combat, making heavier use of raptors, especially armed with meltaguns and plasmaguns, using warp talons and helldrakes.