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?