So, a character died from Draining Kiss of a succubus and his Max HP is 0. Can he be restored by Raise Dead, or does he need a higher level spell? Or a Greater Restoration cast on his lifeless body before Raise dead? I'm probably interested in RAW interpretation, since the character is in Adventurerer's league.
Here's a third answer, because I don't think either of the previous ones are quite correct. As a disclaimer, though, let me note that I don't actively play 5e, so this is just based on common sense and grepping the Basic Rules. It's possible that I may have missed some relevant rule, although I don't think so.
Yes, you can revive a character whose hit point maximum is 0.
This just means that they'll revive with 0 HP, and will therefore be unconscious and start making death saving throws immediately (with a −4 penalty, because they were just raised from the dead).* Since their hit point maximum is 0, they also can't regain any hit points, and they'll die immediately if they take any damage** — but they can stabilize at 0 HP.
The Raise Dead spell description does seemingly contradict what I just said, saying that the raised creature "returns to life with 1 hit point." But I would argue that this cannot override the general rule that (unless explicitly indicated otherwise) "a creature's hit points can't exceed its hit point maximum." Thus, raising a creature with a 0 hit point maximum should leave them with 0 hit points, and no way to gain more.
(I don't think "specific beats general" applies here; for that to be the case, the Raise Dead spell would have to specifically say that it permits a creature's HP to be raised above their max HP (or that it raises their max HP), which it doesn't. Compare this e.g. with the various healing spells, whose descriptions all just say that the target "regains X hit points," with the clear but unstated assumption that the target's HP are still implicitly limited by their hit point maximum, since the spell does not specifically override that.)
Still, presuming that the character you've revived won't take any damage, they won't die again until they suffer three death saving throw failures. This should give you enough time to e.g. cast Greater Restoration on them to restore their max HP, or (if you can't do that immediately for some reason) stabilize them until you can fix them properly.
Ps. The Draining Kiss ability also says that the victim will regain their max HP after a long rest. However, the rules on taking a long rest say that:
A character can’t benefit from more than one long rest in a 24-hour period, and a character must have at least 1 hit point at the start of the rest to gain its benefits.
It seems pretty clear to me that the termination of the Draining Kiss effect should count as a "benefit" of the long rest, and therefore that one cannot recover from being drained to 0 max HP just by (being raised from the dead, stabilized and then) resting.
That said, if a spell like Greater Restoration is not available, I suppose one could instead use the 2nd-level abjuration spell Aid*** to temporarily raise the victim's HP and max HP to 5 for 8 hours, just enough to let them take a proper long rest at positive HP.
*) As noted in the comments below, there's an argument to be made that the revived character should be automatically stable at 0 HP, since they were not reduced to 0 HP by taking damage. On the other hand, it can also be argued that they should be unstable by default, since they haven't been stabilized through first aid or by succeeding on three death saving throws. It really depends on whether you assume to be the default state for creatures that end up at 0 HP without taking damage, something that at least the Basic Rules don't seem to explicitly state. Personally, I'd assume it to be unstable, if only because the Basic Rules first categorically state that "[w]henever you start your turn with 0 hit points, you must make [a] death saving throw", and only later describe stabilization as an exception to that, but it's possible that other rules describe it differently. In any case, I don't see it making much of a difference in the end; even if the character is revived unstable and consistently fails their death saves, there should be enough time for whoever raised them to heal and/or stabilize them before they die again.
**) There's a bit of a curious edge case here. The rules say that you die if you're at 0 HP and take damage equal to or greater than your max HP. Thus, even zero damage should be enough to kill a character with zero max HP; but the rules also pretty clearly imply that this rule is checked only if and when the character in fact does take damage. Off the top of my head, I'm not sure if there's any way in 5e for a character to take damage, with the amount of damage being zero — but if there is then, arguably, even this should be enough to kill a character with zero max HP. They're literally teetering just at the edge of death, with even an infinitesimal push being enough to send them over.
***) It's not totally clear to me whether the HP granted by the Aid spell are "temporary hit points" in the specific sense used by the rules, and apparently I'm not the only one who's confused. Still, even if they are temporary HP, and thus won't raise the 0 HP character to consciousness, it seems to me that they should still grant them the ability to take a long rest.
Raise dead will raise the character, character will be stable at 0HP until a long rest.
Death kiss to 0 max hp is more specific that raise dead which grants 1hp. Raise dead removes any non-magical diseases and poisons, but does not neutralize magical effects. This prevents the gain of one HP.
HOWEVER rules for death on PHB page 197 States:
A stable creature doesn't make death saving throws, even though it has 0 hit points, but it does remain unconscious. The creature stops being stable, and must start making saving throws again if it takes any damage.
Since having a max of 0 HP is not a cause of 1hp damage from raise dead, but rather just prevents the 1HP gain, the raised character is alive, has zero hit points, but remains unconscious. They are however alive and stable.
Once the character can take a long rest (per deadly/draining kiss), the character will be fine. If the character cannot take a proper long rest, however they will remain unconscious until the party can rest properly. They cannot gain the 1hp in 1d4 hours of being stable because the max 0 hp prevents that from happening.
Can he be restored by Raise Dead, or does he need a higher level spell?
Yes he can be restored, and the Maximum HP becomes 1.
From the wording of Raise Dead:
You return a dead creature you touch to life, provided that it has been dead no longer than 10 days. If the creature's soul is both willing and at liberty to rejoin the body, the creature returns to life with 1 hit point.
Then you can cast Greater Restoration on him to return him to his normal hit point Maximum.
[Can] Greater Restoration [be] cast on his lifeless body before Raise dead?
Technically no, since dead things aren't creatures and Greater Restoration requires the target to be a creature.
You need to cure the Maximum HP drain first.
Raise Dead (PHB, p. 270):
This spell doesn’t, however, remove magical diseases, curses, or similar effects; if these aren’t first removed prior to casting the spell, they take effect when the creature returns to life.
Draining Kiss is definitely a "similar effect", so it would need to be rectified (via, as you say, greater restoration) before a raise dead would be effective.
What happens if the character is raised without first removing the effect?
Draining Kiss (Succubus/Incubus MM, p. 275):
The target’s hit point maximum is reduced by an amount equal to the damage taken. This reduction lasts until the target finishes a long rest. The target dies if this effect reduces its hit point maximum to 0.
Raise Dead normally will give the newly-raised character one hit point, but Draining Kiss has the more specific effect of changing the character's hit point maximum to zero. Characters with zero hit points are normally alive, unconscious, and stable. But, again, Draining Kiss has a more specific effect: if their maximum HP is zero because of Draining Kiss, they're dead.
A character who has been dead and then raised hasn't completed a long rest (which would remove Draining Kiss's HP max reduction), and Raise Dead explicitly doesn't remove effects like this, and states that they will affect the creature when it returns to life. A character killed by having zero maximum HP from Draining Kiss who is raised will be affected by the Draining Kiss effect as soon as they return to life, and, having zero hit points, they will immediately die.