The fifth-edition Monster Manual includes listings for two “dragons” that aren’t individual creatures per se but rather templates that can be overlaid on any chromatic or metallic dragon stat block. Shadow dragons are dragons that have made lairs in the Shadowfell—a parallel plane of existence full of negative energy, dreary and desolate—and suffered the sorts of effects you’d expect from living for decades or centuries in such a place. Dracoliches are dragons that, like humanoid liches, have turned themselves into undead horrors in the misguided pursuit of immortality.
Shadow dragons and dracoliches are created by applying certain modifications to the stat block of an adult or ancient dragon of another type, either chromatic or metallic. (Yes, it seems that even metallic dragons can become shadow dragons or dracoliches, supposing that they were subjected to some sort of sufficiently powerful corrupting influence or curse.) Let’s look at what effects these modifications might have on their combat tactics.
Shadow dragons have increased proficiency bonuses in the Stealth skill, along with the Shadow Stealth and Sunlight Sensitivity features. Shadow Stealth grants the ability to Hide as a bonus action; Sunlight Sensitivity imposes disadvantage on attack rolls and Wisdom (Perception) checks in daylight. So here’s our first difference: Shadow dragons won’t come out during the daytime. They’re strictly nocturnal and subterranean.
Despite their having the same “brute” melee-fighter profile as other dragons, Shadow Stealth gives them an incentive to fight in a more skirmishy style: Attack, retreat, Hide, repeat. Their high Constitution, armor class and hit points will make them unconcerned about the opportunity attacks they might incur by retreating. However, I don’t think it would be very much in character even for a corrupted dragon to fight this way every round. Maybe have it switch from slugfest to skirmish if it’s having trouble landing melee blows, or if its foes are landing too many or are surrounding it too easily.
The other alteration that might affect a shadow dragon’s tactics is Shadow Breath, which turns all damaging breath weapons into waves of necrotic energy with the potential to turn enemies into undead thralls. This gives the shadow dragon an incentive to focus its attacks on its less durable foes. Identifying these foes requires a certain measure of Intelligence, however, one that former blue, green, red and metallic dragons are likely to possess; former white dragons, not so much.
The MM gives the dungeon master the choice of whether or not to allow a shadow dragon to use the lair actions of its former type. In general, I find, the debilitating lair actions of chromatic dragons fit neatly with the shadow dragon concept; movement-restricting lair actions reasonably well, with modifications to their flavor; and direct-damage lair actions less consistently well. The black dragon’s stinging insects have an echo in the mummy lord’s insect plague spell, and a green shadow dragon could generate dry, gnarled, thorny roots, but I think a blue or red shadow dragon would lose its ability to generate lightning or raise magma. Metallic dragons’ lair actions all fit adequately enough with the shadow dragon template.
Aside from these alterations, shadow dragons have no compelling reason to fight differently from adult or ancient dragons of their original types.
The dracolich template, to my disappointment, offers even fewer interesting modifications to dragon behavior—which is to say, none, really. Like the shadow dragon template, the dracolich template can be applied only to an adult or ancient dragon. And what does it offer? Resistance to necrotic damage. Immunity to poison damage and to being charmed, frightened, paralyzed or poisoned. Immunity to exhaustion. Resistance to magic. That’s it. Nothing that enhances what it can do, only features that take away from what you can do to it. Boooo-ring.
So, obviously, a dracolich is going to fight the same way it did when it was a living dragon, even to the point of fleeing when it’s seriously injured. It didn’t go through all the trouble of becoming immortal just to be wasted by a group of punk “adventurers.” If they’re capable of dishing out that much damage, it would rather be someplace else. Yeah, if its physical form is destroyed, its phylactery gives its soul a place of refuge until it finds a new body to inhabit, but that’s a pain, and in the meantime, someone might find the phylactery and destroy it. Not a chance worth taking.