Skip Beat! (2011)

Jang Joon Hyun is a talented and popular musician. He looks down upon the traditional trot music genre. Meanwhile, Choi Chun Hee works multiple jobs as the breadwinner to support her father and younger sister. Her mother was a trot singer and she inherited the voice, along with hopes of being a trot singer herself someday. A romantic relationship begins between these two individuals.

Female lead who follows their childhood male friend to another city only to be disappointed by him.
Female lead learns, grows and works on improving herself into a confident individual for her own sake.
Male lead falls in love female lead while helping her.

the main female protagonists are very similar both are a bit quirky and very silly while frightening to people around them sometimes. Also i think it's funny how seriously the situations which could be fairly simple are taken.

Woo Hyun is a Korean man, and Haruka is a Japanese woman. They live different lives, but they both carry emotional scars from their first love. While looking for answers and hope, their fateful encounter will change their lives. It started with one message… Haruka, a stage actress in Seoul, has been in a slump ever since she broke up with her first love. She cannot forget him and keeps sending messages that go unread on LINE. Despite her emotional hurt, Haruka wants to believe in love. In Tokyo, Woo Hyun, an aspiring movie director, keeps on doing interviews concerning “love”. After being deeply hurt by his girlfriend, who thought about getting married, he no longer believes in love. Haruka and Woo Hyun have both grown timid of love. The two of them, who live apart in Tokyo and Seoul, have a chance encounter because of a LINE message delivered to Woo Hyun’s smartphone from Haruka. They exchange messages without knowing each other’s faces and are drawn to each other before they realise it

both have a female lead who follows and help
their childhood male friend

Both are about women who are dumped by their superstar boyfriends. Skip Beat! is more about revenge against ex-boyfriend, whereas Lovesick is more about getting over ex-boyfriend (kinda).

High school graduate Gong Xi gives up her chances for university in order to support her childhood friend and romantic goal, Bu Po Shang, in his pop idol career. Upon arriving in Taipei, Gong Xi starts working on multiple jobs in order to support Bu Po Shang, whose popularity quickly rises, eventually becoming one of the top idols in Taiwan. One day, Gong Xi catches Bu Po Shang flirting with his manager, and learns that he only used her so she can help him with his living expenses. Heart-broken and betrayed, Gong Xi vows to get revenge by becoming a bigger star than him. Gong Xi auditions for L.M.E., Bu Po Shang's rival talent agency, and joins L.M.E.'s new-found department "Love Me". At L.M.E., Gong Xi meets famous actor Dun Helian, who eventually falls in love with her. ~~ Adapted from the manga “Skip Beat!” by Nakamura Yoshiki

Choi Si Won as main role again. Although he is arguably completely different in this drama (as he is even speaking a different language), he is just as amazing in this! I recommendand it completetly!

High school graduate Gong Xi gives up her chances for university in order to support her childhood friend and romantic goal, Bu Po Shang, in his pop idol career. Upon arriving in Taipei, Gong Xi starts working on multiple jobs in order to support Bu Po Shang, whose popularity quickly rises, eventually becoming one of the top idols in Taiwan. One day, Gong Xi catches Bu Po Shang flirting with his manager, and learns that he only used her so she can help him with his living expenses. Heart-broken and betrayed, Gong Xi vows to get revenge by becoming a bigger star than him. Gong Xi auditions for L.M.E., Bu Po Shang's rival talent agency, and joins L.M.E.'s new-found department "Love Me". At L.M.E., Gong Xi meets famous actor Dun Helian, who eventually falls in love with her. ~~ Adapted from the manga “Skip Beat!” by Nakamura Yoshiki

Traversing the cities of Berlin, Seoul, and Tokyo, a 10-year-long love story between two young men is told. It all starts when Ryu Narutaki, who left everything behind in Japan, is saved by a boxer named Johan Hwang in a foreign land.

High school graduate Gong Xi gives up her chances for university in order to support her childhood friend and romantic goal, Bu Po Shang, in his pop idol career. Upon arriving in Taipei, Gong Xi starts working on multiple jobs in order to support Bu Po Shang, whose popularity quickly rises, eventually becoming one of the top idols in Taiwan. One day, Gong Xi catches Bu Po Shang flirting with his manager, and learns that he only used her so she can help him with his living expenses. Heart-broken and betrayed, Gong Xi vows to get revenge by becoming a bigger star than him. Gong Xi auditions for L.M.E., Bu Po Shang's rival talent agency, and joins L.M.E.'s new-found department "Love Me". At L.M.E., Gong Xi meets famous actor Dun Helian, who eventually falls in love with her. ~~ Adapted from the manga “Skip Beat!” by Nakamura Yoshiki

L, an angel who’s endlessly fascinated with the human world, gets into trouble when she unthinkingly saves the life of Han Shi Yeong, a man who was meant to die. To make up for her mistake she must guard him on Earth for one hundred days and keep him safe from Hwan, a death god who is required to collect his soul. Both supernatural beings must contend with the knowledge that whichever one of them fails by the end of the hundred days will be erased from existence, and the longer they stay on Earth the further their powers fade and the more human they become.

High school graduate Gong Xi gives up her chances for university in order to support her childhood friend and romantic goal, Bu Po Shang, in his pop idol career. Upon arriving in Taipei, Gong Xi starts working on multiple jobs in order to support Bu Po Shang, whose popularity quickly rises, eventually becoming one of the top idols in Taiwan. One day, Gong Xi catches Bu Po Shang flirting with his manager, and learns that he only used her so she can help him with his living expenses. Heart-broken and betrayed, Gong Xi vows to get revenge by becoming a bigger star than him. Gong Xi auditions for L.M.E., Bu Po Shang's rival talent agency, and joins L.M.E.'s new-found department "Love Me". At L.M.E., Gong Xi meets famous actor Dun Helian, who eventually falls in love with her. ~~ Adapted from the manga “Skip Beat!” by Nakamura Yoshiki

High school graduate Gong Xi gives up her chances for university in order to support her childhood friend and romantic goal, Bu Po Shang, in his pop idol career. Upon arriving in Taipei, Gong Xi starts working on multiple jobs in order to support Bu Po Shang, whose popularity quickly rises, eventually becoming one of the top idols in Taiwan.
One day, Gong Xi catches Bu Po Shang flirting with his manager, and learns that he only used her so she can help him with his living expenses. Heart-broken and betrayed, Gong Xi vows to get revenge by becoming a bigger star than him. Gong Xi auditions for L.M.E., Bu Po Shang's rival talent agency, and joins L.M.E.'s new-found department "Love Me". At L.M.E., Gong Xi meets famous actor Dun Helian, who eventually falls in love with her.

~~ Adapted from the manga “Skip Beat!” by Nakamura Yoshiki

The female leads are both fighting for their dreams and end up in a cleaning job. Both female leads encounter a male lead they do not get along with at first.