I am helping an elderly lady financially, who has taken on her granddaughter. Her granddaughter's dad was killed and her mom lost custody due to drugs. I suppose she is considered an orphan. I discussed with grandmom the need to become a Christian. She said she was baptized into the Lord's church years ago and understood the need to return. I told her I would give her gas money, if needed, to attend church. She attended a few times but hasn't been back in a couple of months. Since December, I have given her easily over $1000 for rent or electricity. Now she is wanting $400 for rent. I see no end in sight for her financial needs to be met. She has a part-time job and her daughter is drawing a disability check. Is it my Christian duty to support this lady? I would feel better about the situation if I knew this is what God expects of me. I am in education, which will give you an idea of my income.
You've made two mistakes. A too common practice in the denominations is to offer "incentives" to get people to come to church. Yet the only thing God has offered to draw people is the gospel. "No one can come to Me unless the Father who sent Me draws him; and I will raise him up at the last day. It is written in the prophets, 'And they shall all be taught by God.' Therefore everyone who has heard and learned from the Father comes to Me" (John 6:44-45). But when people don't respond, some want to "help" God along by offering something else. That was the mistake the rich man made.
"Then he said, 'I beg you therefore, father, that you would send him to my father's house, for I have five brothers, that he may testify to them, lest they also come to this place of torment.' Abraham said to him, 'They have Moses and the prophets; let them hear them.' And he said, 'No, father Abraham; but if one goes to them from the dead, they will repent.' But he said to him, 'If they do not hear Moses and the prophets, neither will they be persuaded though one rise from the dead'" (Luke 16:27-31).
You are seeing the truth of this statement. Even with a paid way to services, this woman chooses not to come. Consider the points made in the article "Did Jesus Use Carnal Methods to Attract Crowds?"
The command "Pure and undefiled religion before God and the Father is this: to visit orphans and widows in their trouble, and to keep oneself unspotted from the world" (James 1:27) contains deeper meaning that simply throwing money at a problem and hoping it will go away. Helping this woman find a better paying job or finding the child a place to stay so the woman could work longer hours would go further to help solve the problem. What is happening instead is that she is now factoring in your gifts as part of her income in determining how much to spend each month. If you want to help a poor family in this manner by your own free will, that's fine; but it appears you can't and you're feeling trapped. Gifts are supposed to come from the excess God has given to us. "Let him who stole steal no longer, but rather let him labor, working with his hands what is good, that he may have something to give him who has need" (Ephesians 4:28).
Sadly, this woman told you that she has left the church, which explains a lot about her raising a daughter who became a drug addict. Do things that benefit the child instead, who is the innocent victim in this tragedy. I don't know how old the child is, but see that clothing is provided. Offer rides to church. Find things the child needs and arrange to get them. That is what "visit" actually means. Get involved in the child's life enough to see that his needs are met. If grandma isn't able to support the child, then offer to help her find a home for the child.