Does my Zakāt obligation lapse if I gave my money to my older brother to deliver to my poor brother, but he took the money for himself, knowing that it was Zakāt, and I have demanded the money from him but he is procrastinating?

For Zakat (definition) to be valid, it is a condition that the recipient be enabled to possess it and that ownership of it be transferred to him. If the Zakat perishes in the hands of the agent before its delivery, then it is at the risk of the owner of the wealth, due to the non-fulfillment of the commanded giving mentioned in His (the Most High) saying: (And give the Zakat). Accordingly, the questioner's obligation of Zakat has not been discharged, and he must take it from his brother or give it out again.