What does "lean forward" means in that context
Solution 1:
In 2013, Sheryl Sandberg, the chief operating officer of Facebook published a book titled, "Lean In: Women, Work, and the Will to Lead".
There's also an associated website, LeanIn.org
The book is meant as career advice for women, especially those in traditionally male-dominated businesses. The advice to lean in means something like: adopt an attitude and a posture that suggests that you're fully engaged - as if you were in a meeting and you were leaning forward in your chair eagerly or aggressively participating.
The phrase, "lean forward," on the poster seems to be referencing that newly popular phrase. The copy writer either got the phrase wrong, was trying to avoid a copyright dispute, or was thought they were being clever.