The Lich can instead prevent others from detecting magic on it.

With use of the spells Nondetection or Mindblank, which guard against divination magic, the Lich can prevent a divination spell like Detect Magic from revealing that the Lich is also under the effect of a spell such as Alter Self or Disguise Self. Adding Nystul's Magic Aura into the mix will also protect the Lich from effects like a Paladin's Divine Sense that might reveal that it is an undead. Because Nondetection, Mindblank, and Nystul's Magic Aura are all non-concentration spells, the Lich could have all of them cast on himself in addition to Alter Self or Disguise Self, making him appear human to both physical and magical senses.

Fabricate a flesh suit.

If the goal is just for him not to look like a walking skeleton, he could make a disguise using fabricate and a fresh corpse.

Fabricate won't transmute creatures, but the corpse is dead, and the lich is not actually modifying himself; he can put the mask on his face with glue or something. This will look wrong to anyone who watches him speak or otherwise move his face, so he'll be disguising himself as someone who's been badly disfigured. He'll need a cover story for that.

(Personally, I'd have him spread the rumor that he has leprosy or something. This will both explain his disfigurement and deter anyone from taking a really close look at him.)

One of the reasons I like this is that it gives him a disturbing behavior pattern: the suits don't stay fresh, so every time he wants to meet with you, he has to make a new one, and one of the castle servants (or some other convenient victim) mysteriously disappears and is never seen again, and the other servants will awkwardly deny that such a person ever existed. If you're paying attention you might notice that the Master's eyes are a different color this time.

(I'm assuming fabricate because the reason for avoiding magic is to not have active, detectable spells on himself when he's meeting guests, and in that respect, fabricate is no different from any other way of making the costume. He could use a craft knife and a hot glue gun if he wants, but it's harder.)

I would take a more story-based or setting-based approach. Think about what would qualify as making the antagonist look human in your world, and normal disguises.

For example, if it's common for people to be hooded or cloaked, that's already a simple disguise. What about wearing a mask? Are there any groups in your world that are known for wearing masks? Perhaps certain members of the nobility are known for wearing elaborate masks to show off their wealth or influence. That would effectively hide the face, gloves and boots hide the hands and feet, and human-nobility clothing hides the rest. Then they'd just need to cover the smell of being undead, with non-magical perfumes being sufficient (again, something the nobility would probably have access to).

If this approach would be normal in your world, then the antagonist needs no magic. This outfit might not even qualify as a disguise if it's common enough for certain social classes. It would also allow the antagonist to act within human society in normal circumstances, and they could engage the PCs in dialogue or treachery before combat is even considered. However, if that antagonist is the only person the PCs normally see with a mask, that might be too big of a red flag and the other answers may offer better solutions.

Note that this kind of disguise won't hide the alignment of the antagonist, or protect against spells that specifically detect or affect the undead. But the first protection in such cases could be to have the antagonist act and appear sufficiently normal that using undead-targetting spells doesn't occur to the PCs.

Your desired effect is for the party to be surprised that this NPC is a liche. Your desired means is to pull this off without magic. I'll provide the no-magic answer first, and then follow up with how you can achieve the desired effect with magic.

Without Any Magic

Without magic, we are left with the same mundane options available to you or I here in the real world. Heavy application of makeup might do the trick, which is supported by the Disguise Kit item, a tool that a character could be proficient in per the PHB. The Charlatan background includes a skill for creating a false identity through non-magical means - of course, this is an NPC, so there's no need to constrain yourself with PC building mechanics. Xanathar's Guide provides further rules for the creation of nonmagical disguises:

Create Disguise. As part of a long rest, you can create a disguise. It takes you 1 minute to don such a disguise once you have created it. You can carry only one such disguise on you at a time without drawing undue attention, unless you have a bag of holding or a similar method to keep them hidden. Each disguise weighs 1 pound.
At other times, it takes 10 minutes to craft a disguise that involves moderate changes to your appearance, and 30 minutes for one that requires more extensive changes.

Without the use of Gentle Repose, liches are (probably) in a state of constant decay. The application of a strong perfume could both serve to disguise your NPC and serve as a subtle foreshadowing - your players may later reflect "Oh THAT'S why the strong cologne!"

With Magic, But No Effect

Spells and magical effects that physically alter the NPC's appearance, without leaving an ongoing effect, might not be detectable by Detect Magic. Note that True Polymorph, after one hour, is "permanent", no mention of "until dispelled". This suggests that the spell completely changes a creature, and that the effect is not sustained by magic and therefor not detectable but spells that divine the presence of magic.

Disguise Magical Effect

user48255 has more information on this.
Nystul's Magic Aura's mask ability can disguise the lich's creature type. If asked why the NPC has any magical effect at all, they can explain that it's an unfortunate curse, a divine blessing, a spell of protection, etc - you want to give your PCs some kind of hint or foreshadowing, right?

Hiding the magic aura

As several people have pointed out, this is probably the simplest method, and the most sensible as well. After all, the lich likely has to hide from other people too.

Magical double bluff

Have the NPC be wearing some other spell, ideally illusion, either openly, or known to the PCs. They can detect that, but not know what's hiding behind it. Especially if it were supposedly changing something about him other than his face.

Mundane double bluff

The same might work if he wore a full face mask or similar: they'd know he was hiding something but not what.

Misdirection

Are they likely to detect magic? Can you set things up so they probably won't?

New Lich

Depending how the details of lich-ing work, is it possible he was in the process of becoming a lich, and was human when he met them?

Planning a satisfying revelation

For all these answers, be aware of how revelations often unfold in roleplaying games. Ideally have a few pieces of information they might eventually learn (he's a lich, what his plan is, etc) And some clues which might or might not lead there. E.g. "you detect an illusion spell on him but don't know why".

And then, don't try to force the plot to make sure they don't find out, try to make it work so that if they twig immediately that he might be a lich, then praise them, and work on a different big reveal later. They won't get ALL of them.