As part of artist Miranda July's ''We Think Alone'' project, the 27-year-old actress shared an email she wrote to the fun guitarist in October 2012 while she was on a trip to India, in which she revealed the depth of her feelings for him.
Writing about walking through a garden and spotting a couple chatting together, she said: ''We spent 40 minutes walking around the garden and when we circled back they were still there, chatting like fiends.
''And I thought of you, like always, and I felt I could spend four days on a bench with you and it wouldn't be enough time to hear all the stories you have to tell. I literally want to know everything you have ever seen and what you felt like while you were seeing it. And I will be so much better my whole life for knowing those things.''
Lena previously revealed her taste in men has changed in recent years and she is now madly in love with Jack.
She said: ''When I was younger, I liked men who gave me some guff. Now I'm much more into someone who is interesting and open with his emotions has a passion for what he does, wants to hang out with my parents and doesn't want to stay out too late.
''If I can get excited imagining funny things he did as a kid, there's a pretty good chance I'm in love with him.''
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