Similar concepts. BOAB follows a woman in fulfilling her wish to become beautiful through plastic surgery.

-Erased is also an anime that I highly recommend, since it would probably be less rushed than the movie. In Japanese, it is 'Boku Dake Ga Inai Machi'-

-both include male roles who are not the most popular in school
-both include time travel
-both are to save the death of a girl they like
-both have the sam vibes but erased is a bit more in the mystery category.

Although LNF follows the story of two adults loving after having a child, OMGB follows the story of the child and has similarities with both parents wanting custody. Both gave me similar vibes though, even if OMGB is much less romantic and much more slice-of-life melodrama-y (child had childhood alzheimers).

Both include a broken slightly messed up family.

Both have slightly pathetic adults.

Both include an unconventional outsider. A tutor in Kazoku Game and a Housekeeper in The Suspicious Housekeeper.

Both have very good character developement.

(Please note that the suspicious housekeeper is a korean drama)