In Fake Fact Lips by Machi Suehiro, Ryo and Zen have been competing since high school. Ryo feels pressure by his father. Zen is trying to make his mark after growing up in his older brother's shadow. Zen is belligerent and self-conscious but his achievements are honestly pursued. Without realizing the impact of his words, Zen encourages Ryo to compete for the same reason. Rather than trying to satisfy a father who can never be satisfied, why not make Zen his rival?
Ryo does, especially after he realizes that competition is a form of communication with Zen.
I have my doubts about competitive lovers. When does the competition cross the line into dysfunction, as in the CSI episode where the boyfriend causes his girlfriend's death when he redraws her hiking map? When does competition simply become too wearisome?
Fake Fact Lips works for several reasons: Ryo and Zen are honest with each other; the competition continues to be a language of connection and flirtation; the competition is healthy in the sense that it involves achievement (constructive results) rather than negation (destructive or absent results).
The healthy form of competition here is quite common in manga. In Yuri on Ice, competition inspires the two lovers as well as binding them together. In Free, which has no romance, competition inspires the somewhat drifting Haruka Nanase to connect to his future.
Like with all frenemies, however, the competition could go sour. As long as it doesn't...it works!