Lena was trying to respect Walter as the man of the house. Often, Walter is dominated by feminists in the novel. He has yet to take charge and run the family as head of the household. Lena has been in the leadership role as head of the house. Lena is beginning to see what this has done to Walter and his masculinity. Walter needs to be in charge for once. Lena believes that giving the money to Walter will heal his hurts from having been subjected to dominant female leadership.
When Lena gives her son Walter the money, he even responds by asking if she really trusts him. Walter is touched by his mother's trust in him. However, Walter still makes a bad business deal. He trusted Willy Harris. In the end, Walter loses all the money. As it turns out, it was a bad idea to trust Walter with the money.
Of course, there did finally come a change in Walter by the end of the story. He takes a leadership role and "comes into his manhood" as Lena calls it. Walter informs Karl Lindner that they will indeed move into the house in the white neighborhood. He promises to be good neighbors. Lena and Ruth are so proud of him.
Lena gives Walter the $6500 that is left after she puts a $3500 payment down on her house because she wants him to know that she trusts him and will empower him. She says to Walter, "I been doing to you what the rest of the world been doing to you." She understands that Walter feels emasculated by the way the world treats him, and she wants to empower him by letting him know that she trusts him. Lena doesn't know whether Walter is trustworthy or not, but she knows that she has to show him that she thinks he's trustworthy if he is ever going to become more mature.
Walter proves untrustworthy, as he gives the money to someone who runs away with it. Although Lena tells him to put Beneatha's share of the money in the bank, he doesn't do so, and he loses Beneatha's money for school. In the end, however, Walter proves himself more mature when he doesn't accept money from white house owners to stay out of the new neighborhood the family is moving to. Though Beneatha is more trustworthy than Walter, Lena doesn't give her the money because Beneatha already has a great deal of confidence in herself. Even if she doesn't have the money from her father's insurance policy, Beneatha, Lena knows, will make something out of herself because she is confident, intelligent, and brave.