"They're over – they've broken up," a source says. "They split after Thanksgiving weekend."
Adds another source: "She is concentrating on her life and her career."
Lohan, 21, checked out of the exclusive Cirque Lodge on Oct. 5. She had been there since August. (The breakup was first reported by E! News.)
A week after his daughter had left Cirque Lodge, Lindsay's father, Michael Lohan, told PEOPLE about Giles: "He's a great, great kid. If you met him, you'd like him."
New Record LabelOn the career front, Lindsay is gearing up to head back to the studio to record an album for Universal Music Group's Motown label, to be released next year. (She had previously recorded with the parent company's Casablanca label.)
A label source tells PEOPLE that Lohan "is expected to start recording within the next two weeks."
In addition, Lohan is gearing up for a scheduled cameo on ABC's Ugly Betty. Says her rep: "As we left it, she was in talks to do an arc on Ugly Betty, which she is a huge fan of. She's hoping that the [writers'] strike ends soon. She'd love to get back to work."