And I'm not talking about she just gets engaged, either she gets really close to marriage or does get married. She's in love with the male lead and they have to deal with this.

I can think of a couple where she is forced to marry the male lead, but do I understand it right you want the female lead to marry another guy?
mary stayed out all night
For what I understand is that she gets married (or almost gets married) to the guy but is in love with other guy, so


Que sera sera
Knock knock loving you
The princess' man
Goong
Mary Stayed Out All Night
FullHouse