Is it possible for a Half-Dragon's alignment to change from their dragon's alignment type? For example, if a blue Half-Dragon (Lawful Evil) had an alignment-affecting spell cast on them, or was bitten by a lycanthrope of a different alignment, would their alignment change?
First of all, half-dragons are subject to the same alignment rules as their draconic parent:
Just so that’s clear.
Dragon Alignment, and creature alignment in general
Dragons, like many creatures, have alignments that are listed as “Always” one thing or another. Black dragons are “Always Chaotic Evil,” gold dragons are “Always Lawful Good,” and so on.
But this is a misnomer. “Always” does not mean “always” here. It actually means “almost always.” Page 305, Monster Manual:
So there you go. Yes, it is possible for a half-dragon to have a different alignment. It’s rare and exceptional, but then in most games, so are player characters.
Note that “Always” implies an innate, biological pressure to be that alignment (cultural pressure for a given alignment is typically the “Usually” category); being raised in a generally Chaotic Good elven village is still going to leave a half-blue dragon elf feeling strongly pressured to be Lawful Evil; only a rare individual in that circumstance would be able to embrace his non-dragon heritage so thoroughly as to adopt its alignment despite his biology.
As long as a creature is capable of having an alignment at all, alignment-changing magic will work on it. It's magic; this is what it does.
It is very difficult for a creature "born into" an alignment to change its alignment without magical assistance, but it's not actually against the rules. No official explanation is ever really given for this, but Wizards' own Eludecia the Succubus Paladin gives one possibility: creatures born into an alignment essentially feel instinctive urges to behave in ways that pull them in that direction, and these urges do not go away just because the creature has tried to change its outlook.
Magic can remove those urges, and I think it's safe to assume that this is exactly what happens during a magically-assisted alignment change. But willpower alone won't take them away, and so a creature born into one alignment that tries to change to a different alignment is going to be fighting her own psyche for the rest of her life. I cannot imagine that it would be as difficult for a half-dragon to change its alignment "the hard way" as it would be for a full-blooded dragon, but I don't think it's hard to argue that it should still not be easy. I know of no rules to deal with it, but there's an excellent opportunity to roleplay here.
Under this interpretation, lycanthropes may face the reverse problem. The recently-afflicted can be of any alignment, but the instincts of their particular affliction will immediately start trying to pull them toward the usual type. Few people can hold out against that forever, especially during involuntary changes.