Here Lanyon gives an extremely short summary of the events of the prequel comic Bleeding Heart. For anyone planning to read Bleeding Heart who hasn't yet, don't worry--he's not spoiling the whole story. He doesn't even know the full story, as some of it happened exclusively to Jekyll. He's also leaving out the events that occurred before and after Bleeding Heart, which will be explored in this story, but not yet.
Several readers have questioned the idea that anyone would seriously think that Hyde is Jekyll's illegitimate son. This is an idea from Strange Case, though it is admittedly more plausible in the original, where Jekyll is aged somewhere in his fifties. (In my defense, almost all adaptations age Jekyll down!) Most people estimate Hyde to be late teens/early 20s, which makes it just barely possible that Jekyll could have fathered him at age 19 (when he met Morcant). Lucy is more inclined to believe the illegitimate-son-blackmailing-his-father theory since Rachel describes Hyde as a literal baby half the time.
By the way, Rachel is mostly just messing around with her fanfiction-y theories about Jekyll and Morcant's OTP lovechild, but it does give her a convenient excuse to cinnamon-bun-ify Hyde more and also conveniently shut down any serious inquiry into Hyde's true identity.