According to reports, the actress has moved Matthew into her house in the Hollywood Hills in California after four months of dating.
A source told People magazine that Lea and Matthew, an actor and model, are "really happy" and "make a great team."
Neither Lea nor Matthew have commented.
It's thought they met for the first time on the set of Lea's music video for 'On My Way' back in April and romance later blossomed. Since then, they've been spotted out and about together on several occasions.
Earlier this week, gorgeous Lea glammed up the red carpet at the LA premiere of the new season of Sons of Anarchy.
Lea sizzled in a plunging, low cut white dress, showing off her holiday tan following a recent birthday trip to Mexico.
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