Is it permissible to justify asking a wealthy person for money based on a personal need, when the true intention is to help a needy, ill, widowed neighbor pay for an operation?

If you are in need of money, there is no harm in asking him for help, and the money would then be yours to dispose of as you wish, and you could use it to help your neighbor. However, if you are not in need of it, then it is not permissible for you to lie and claim need. It is better to inform him directly of your neighbor's need for assistance.