Liches voluntarily destroy their soul in a mad attempt to achieve immediate power and material immortality at the expense of spiritual immortality and long-term gains. Generally, you can't do that and not end up evil in most D&D settings.
Historical background. Lich is an old English word for "corpse"; the gate at the lowest end of the cemetery where the coffin and funerary procession usually entered was commonly referred to as the Lich Gate.
Lich's phylactery
A magic phylactery was used to store the souls and life force of liches. A mage had to create such a phylactery in order to become a lich, a highly expensive and taxing effort. Typically, a phylactery was a sealed metal box containing strips of parchment on which arcane phrases were inscribed.Depending on the method of becoming a lich, a lich can be of any alignment, retaining whatever alignment it had in life. Good liches are presented in Monster Compendium: Monsters of Faerûn, a supplementary rule book for the D&D 3rd edition rules.
No, Voldemort is not a lich, and the justification is quoted in your question. However, in ALL of these, while the use of a phylactery to house the soul is common (and replicated to some degree by JKR), the main requirement is that the person becoming a lich actually die. The lich is an undead being.
Since a lich's soul is mystically tied to its phylactery, destroying its body will not kill it. Rather, its soul will return to the phylactery, and its body will be recreated by the power keeping it immortal. Thus the only way to permanently destroy a lich is to destroy the phylactery as well.
A lawful evil lich craves the power to dominate others. A chaotic evil lich craves the power to destroy. A neutral evil lich may want one or the other, or both. Domination is the purview of a dark overlord, and is a perfect desire for a campaign-ending lich.
According to one of the items in 5e's DMG called the Book of Vile Darkness, there is a spell that one can learn in there to become a lich or a death knight, but only wizards can learn spells so your DM may (or may not) homebrew a system for Warlocks to become liches.
In fantasy fiction, a lich (/ˈl?t?/; from Old English līċ meaning "corpse") is a type of undead creature. Liches are depicted as being clearly cadaverous, bodies desiccated or completely skeletal. Liches are often depicted as holding power over hordes of lesser undead creatures, using them as soldiers and servants.
Alignment. Depending on the method of becoming a lich, a lich can be of any alignment, retaining whatever alignment it had in life. The D&D version 3.5 Monster Manual, a core D&D rule book, emphatically states that liches are always evil, but there are references to good liches in other manuals.
D&D co-creator Gary Gygax credited the inspiration for the alignment system to the fantasy stories of Michael Moorcock and Poul Anderson.
