Not all that goes by the name of “romance” is full of lipstick! A good bit has hardly any sex in it, too.
I second the recommendation for Diana Gabaldon’s series. It’s sturdy enough that you’ll find it in the literature section now.
This is the “medievel time travel” genre. Lynn Kurland has a series similar to this, but they are lighter in tone, contain more humor, and there are worthwhile dudes, both medieval and contemporary, in them. There is little sex.
From this Moment On involves no time travel, but a really funny case of mistaken --and not so mistaken – identities and undeserved reputations. I think your son will be easily able to see himself as Colin of Berkhamshire, aka “The Butcher of Berkhamshire,” and enjoy the goings-on.
You’ll see all of this series listed in the back of any of the later novels, so you can find the earlier ones easily. Also by the publication dates on Amazon.com. You don’t have to read them in exact order, but the first few do explain some things that occur in later novels.
Pretty much anything by Lynn Kurland is good. Her recent series involves a mythical land of Tor Neriche. Star of the Morning, The Mage’s Daughter, and Pricess of the Sword. Very light and possibly a lot like an anime (although I have not read an amime, so have no way to know for certain).
If he liked Harry Potter, he might enjoy a series about a sort of grown-up Harry Potter . . . Harry Dresden, who is a wizard in Chicago. Jim Butcher is the author. _Storm Fr_ont is the first, and you should read these in order, if possible.
Jim Butcher’s other series, Codex Alera, about a mythical kingdom and a young man named Tavi, with whom your son may identify, is excellent. The Furies of Calderon is the first. They should be read in order.
Lois McMaster Bujold has a space opera series about Miles Vorkosigan, which I highly recommend. Some romance, some adventure, lots about succeeding in life even if you are at a disadvantage. Hard to tell which is the first, but it helps to get started near the beginning. I think there are some lists on Amazon that sort it out.
Her next series beginning with The Curse of Chalion and Paladin of Souls is good.