The two, who were spotted enjoying dinner together on Dec. 30, "are still dating and have been dating," a source close to the couple tells PEOPLE in this week's issue.
"Even though they are both busy, the relationship is solid. They see each other when they can."
The Hunger Games star and Coldplay frontman quietly began dating last August before breaking it off in October.
The source says Lawrence, 24, is at peace with Martin, 37, spending time with his ex, Gwyneth Paltrow, and their kids, Apple, 10, and Moses, 8.
"She understands that the children come first with Chris and his relationship with Gwyneth is based around the family and it will always be a part of his life,” the insider adds. "Things are good between them."
Reps for the couple have not commented.
For more of this story, pick up this week's issue of PEOPLE on newsstands Friday