Some spoilers from the novels

The manhwa is slightly confusing in timelines but the novels clear up some of that.

Egg Benedict was meant to be read first. It's the novel about Kyle (Lyle's younger dominant alpha brother) and Nick (Kyle's beta-turned-omega roomie/bff). Kyle was kidnapped on the eve of his first rut and was forced to be mentally imprinted on the omega son of a human trafficker. Because of this, he is revolted by physical intimacy and is secretly (only to Nick) in love with Nick.

When Nick realizes he's turned into an omega, he sleeps with Kyle but tries to see if it's just pheromones in action so he briefly dates Ash after one of his coworkers introduces them to each other. Ash is an alpha who only dates alpha but he breaks his rules because he falls in love at first sight. They are never intimate because Nick realizes his and Kyle's lives are inseparable. Lyle makes a brief appearance when he sees Nick and Ash together and chastises Nick for hurting his little brother.

That's why in Define the Relationship, Lyle assumes that Ash has a poor first impression of him. Ash only meets up with Lyle as a favor to make Nick happy. When Lyle and Ash meet, it has been eight months since Kyle and Nick married. Lyle remembers that Ash as the alpha he had shared a kiss with 6 years ago, which is also when Ash broke up with Hazel and started to date alphas exclusively. He also remembers Ash as Nick's recent beau.

After Ash and Lyle get engaged, one of Lyle's childhood friends (an aristocratic dominant alpha) confesses his love to Lyle and tries to steal him away. Turns out male alpha can also bear children especially if the spouse is a dominant alpha? But Lyle turns him down. Instead, he and Ash adopt a three year old rescued female golden retriever named Bonbon.