Most recently The Hunger Games star attended on of the musician's performance with Kings of Leon at the Hollywood Bowl earlier this month.
But the whirlwind romance is already over, according to E! Online.
Lawrence previously dated her X-Men: First Class co-star Nicholas Hoult on and off until their split earlier this year, while Martin famously "consciously uncoupled" from his wife of 10 years, actress Gwyneth Paltrow, in March.
Read more:
• Jennifer Lawrence reveals her ideal man
• J-Law slams Perez Hilton for posting nude pics
Late last year Lawrence described her dream man as "somebody to watch TV with me" and who "isn't afraid to fart in front of me."
"I'd rather have just a peaceful time. (Those) are deeper because you can be your true self with somebody, and somebody can be their true self with you," she told the November issue of Vanity Fair.
- WENN