Let me make this clear off the bat: you are in control of the game.
Can your boyfriend be a immortal skeleton throwing fireballs out of his eye sockets? Sure he can.
Will books give you a definitive solution? Nope.
You can have a look at what a Lich is, but this makes him necessarily evil, so you will have to spin this off if that is not the idea.
You can have a look at skeleton creatures, but those are not immortal, so you do have to work out what differs him normal ones.
Liches actually have an artifact holding their soul, pretty much like Voldemort, only he breaks it apart and scatters it around. I don't know any supplement that would give you mechanics for that.
The system is only but a suggestion
I might come in playing the devil's advocate here, but sometimes following RAW is more exerting than things getting out of hand for not following it.
A ex-girlfriend of mine, for instance, found in her first DMing endeavour that for her game group it made more sense to make things up as she went, following RAW for basic mechanics, rather than strictly following rules.
In my group, people are more munchkins and they will create overpowered situations if I do not keep them in check. I would never have guessed DMing could be so freeform, in terms of dynamics, until I met her group.
So if you feel like your adventure is high fantasy enough, you could come up with some achievable way for player to get Voldemort-y.
So feel out your group. Do these people know the system well? Up to what level have they played before? Are they likely to go online searching for complements to find just the gear to make them unbeatable, or more like "I want a magic sword"?
The less munchkins player are, the easier it gets make it as you go.
How hard could it be... Immortality.
If a character could really be immortal in your world, its safe to assume someone would have achieved it already, right? It would be quite a popular thing to go after.
As others have mentioned becoming a Lich is supposed to be a really hard process, and it takes huge maintenance to keep.
Immortality, or something close to it, comes with great price, in nearly any story you pick to base yourself off, and sometimes it just ain't worth it in the end.
Anyhow, granting a player such power at level 1 is way out there. Voldemort is certainly not a level 1 character; your boyfriend's character right now is at most a Tom Riddle learning his first spells.
Can you make this work?
Conflicting groups are a challenge even for seasoned DMs.
What is the nature of your player's desire? It could be very hard to manage a group consisting of 4 Good clerics and a evil murdering skeleton. Aligning expectations here is quite important; if immortality is on the table, it could be the reason for the whole campaign.
Perhaps seeking the tree of life is the quest objective. One will try to use it to heal the village, another wants to study the arcane sigils on it, maybe someone wants to communicate with a dear one through a tea from the tree leaves. Your boyfriend wants to go immortal.
Scale the power up
Since you mention concerns over people getting OP: If someone is too powerful, immortal, or say, gets to convince someone they are actually a circus bear with a Deception roll, throw everyone up a notch.
And let them use their unique OP powers. I had a table once get out of hand because I allowed some players to get demonic or angelic subraces; they had resistance to elements, stat increases, minor spells, you name it. The one that went with a dwarf had nightvision.
His life was miserable in combat compared to others; next time he went unconscious, I gave him a power similar to Lucifer (in the TV series) where he could sense people and their intentions.
While the other players kept getting most of the fun in combat, I gave the dwarf power over all social interactions, something only he could do.
It can get out of hand and you end up with an anime table where everyone is throwing planetary nukes around, but as long as everyone's having fun...
He's your SO so we all like to avoid conflicts, but if your campaign plan is not compatible with that level of power, he, more than anyone else, should be able to play along into the world you want to DM.
After all, role-playing games are a collective adventure, and you're playing as much as they are.