Who was the first woman to ask the Lord for help?

If "the LORD" specifically means the God of the Jews, it was Hagar. She not only pleaded for help in her distress, but accepted that she had behaved badly and agreed to reform. This story is in Genesis 16:1-16.

Sarah also called on the LORD eventually, but not before Hagar did. The fact that she gave Hagar to Abraham as a secondary wife, rather than believing in his promise, actually suggests that she did not trust the LORD at that stage.