Both are a fantastic slice-of-life about a couple maturing through life, separately and together. The chemistry is very strong and depiction of love also felt very real.
Both the main leads are related to their past through an event of tragedy. The theme of unraveling the villain in Hello Monster is more on detective/police setting but in Lawless Lawyer it's more of trying to brace through the loopholes of the justice system. There is more action in the latter, and more psychological elements in the former.