Walter is a dreamer, and he wants to use the money to fulfill of his dream of opening a liquor store. He begs Lena to invest. When Lena puts the money down on a house, as she and Mr. Younger had always dreamed, instead of giving it to Walter, he is so depressed that Lena feels the money interfering with her relationship with her son. She caves and gives him the money.
Again, Walter is a dreamer, but that does not mean Lena could trust him with the money. The issue was that he had no knowledge of business and was obsessed with finding quick solutions for his family's woes, rather than planning carefully and making sure he was associated with the right people. Indeed, he does end up losing the money when the liquor store plan winds up being a scam. Willy Harris, one of his supposed business partners, takes it.
One of the people most hurt by the loss of the money is Beneatha, Walter's sister. She aspires to become a doctor. To her, the money represents payment for her education and a ticket to her bright future. When the money is gone, Beneatha laments that her future and her world had just been ripped out of her hands.
Lena instructed Walter to save a portion of the money for Beneatha's schooling when she gives it to him, but he does not. Lena does not give Beneatha the money directly. Lena is confident that Beneatha will succeed and feels Walter might need more of a push. Lena feels Beneatha simply doesn't need the money; even without it, she'll still make something great of her life.