The Menendez brothers’ possible resentencing is music to Lyle’s first wife’s ears … ’cause she tells TMZ she’s still standing by the pair, despite her own rocky history with her ex-hubby.

Anna Eriksson, who was married to Lyle from 1996 to 2001, tells TMZ that even though Lyle shattered her trust when a misdirected letter revealed he had feelings for someone else, it doesn’t change her stance — she still believes the brothers should be freed.

Anna gives us more insight into her heartbreak, admitting she actually fainted when she found out Lyle was all in for someone else. Even though he wanted to work things out, she wasn’t having it — she says she told him he taught her not to put up with things like that — and she filed for divorce.

Despite not being in touch with the brothers since, Anna still stands by her belief that, at their core, they’re good guys, and she insists you can’t judge them solely by that one tragic act of killing their parents.

Anna also shares that she’s thinking of Lyle’s late grandma — José’s mom — who desperately wanted to see the brothers freed. She says Lyle’s grandma was always so supportive and protective of them, and it was her heartfelt wish to see them be released.

As for herself, Anna says the news that L.A. County District Attorney George Gascón will go to court and ask a judge to free Erik and Lyle is long overdue, adding that sitting through the second trial from ’95-’96 with his family was especially tough.