Sources say father and daughter met recently at the Betty Ford Center, where Lindsay is staying for court-ordered rehab. "She's taking things seriously and she's really had a lot of success so far," says a friend of Lohan. "This is a long road for her with many issues she has to work through. But she's ready to tackle things."
Adds the friend: "Lindsay is now open to working on things with her father. It's a part of her recovery."
Michael Lohan also told PEOPLE after the visit that his daughter, who has struggled with substance abuse problems, is heading in the right direction. "I thank God that she is in the place that she is in now," he said. "And I love her and I am very, very, proud of how far she has come. Really, really proud."
For Lindsay, mending fences with her estranged dad is an important step in the rehabilitation process, a source tells PEOPLE.
"Lindsay really needed to hear it from her counselors how important it was for her to have a relationship with her dad," the source says. "They spent quality time together talking alone."
The Lohan clan, including Lindsay's mother Dina, are expected to show up next week for family day at the center, a time set aside to be "more a healing thing and a bonding thing," according to the source.
And Lindsay's latest stint in rehab seems to be doing her some good, the source adds.
"Lindsay seems totally more clear headed and more focused," the source says. "She's not looking at the future as much as she is the day now. It's day by day with her. Although, she's interested in working, she's more interested in just getting her life together. And she does realize that when she gets out that's going to be a big test for her."
Lindsay's mother Dina Lohan also made strides recently when she finally admitted her daughter is an addict, and said she supported Lindsay's reconciling with her father. "Whatever the facility wishes for her," she said. "It's all about Lindsay and her healing."
Reporting by JENNIFER GARCIA