Any dramas where the female lead leads a promiscuous life before falling in love with the male lead? Maybe after she falls for him, drama is caused by one of her former lovers or something? Maybe some drama happens from her relapsing, but it ends with her and the male lead in a relationship.

HAHAHAHA That title :(((
 
Sorry, I haven't watched any with such story.
the only one I can think of is the Thai lakorn "Dung Sawan Sarb" I haven't seen it though so I can't tell you if it's any good or not
J drama - Nagareboshi is the only one i can think of.

K-drama Little mom scandal sort of fits as well as Cruel City
I know a Philippine movie with this (exact) kind of female lead haha! It's called "Dahil Mahal Na Mahal Kita" or Because I Love You So Much. https://en.wikipedia.org/wiki/Dahil_Mahal_na_Mahal_Kita
Nagareboshi
Bad Love - not really a slut but she dates a married man but then he ends the relationship, then she falls in love with a man that turns out to be the brother of the lover's wife.
Can I just say how much I loved your title? It's the ultimate clickbait (in a good way). 

I'll answer the second part first--dramas where the FL's former lover causes drama:
My Sunshine (cdrama)
General and I (c-drama--not really a lover tho)
Too Late to Say I Love You (cdrama)
Hundred Years Inheritance (kdrama)
Oh My Lady (kdrama...barely barely fits)

As to the first part--the female lead is a player before falling for the male? Yeah, no. The way I see it, more than murder or fraud, the worst crime these female leads can commit is not being "innocent", much less having more than one past partner. Case in point, the examples above are all ex-husbands/fiances. So if there are hits, please post them, yeah?   

Kuzu no honkai - it's the only one I can think of but it's the second female lead and the second male lead
LMAO at the title
Oh I remember one! One of the leads here is promiscuous: My Dear Sister
Kang Yi Na is promiscuous and a gold digger in Age of Youth
Other possible suggestions:

Rental no Koi
Arasa-chan Mushusei

To be honest, I would love to see a woman who is not afraid of her sexuality but is also not portrayed as a slut or promiscuous. That is hard to find in Asian dramas, because they are unbelievable hypocrites. 
not really a slut.. but a gold digger who fools rich old men out of their money ,, she is a model and want to be sponsored

material queen
also there is a kdrama may fit your criteria called  miss ripley
What Ceki said: "To be honest, I would love to see a woman who is not afraid of her sexuality but is also not portrayed as a slut or promiscuous."

My thought exactly. I feel this way about Kuzu no honkai. I feel like that drama really tried, in a way... but couldn't go all the way with it. Also with the main character, she tried to explore her sexuality and all, but I felt like in some scenes her actions/reactions were there to make her conform to the norm. It made it a bit hard sometimes to figure out what exactly she was thinking and feeling. The second female lead on the other hand really enjoyed sex but she was definitely portrayed as a slut and emotionally broken/damaged and a bit "evil" and a bad influence... Her sexuality was even less about her own pleasure than about her need to have control through being adored by men.