Those gifted with lady luck are learning, growing and evolving continuously. You will often find them improving their skills, problem-solving ability, creativity, expertise, experience, and knowledge on a daily basis. This naturally helps them gain access to all the necessary resources that allow them to attract seemingly lucky events into their lives.
I like this book and have been returning to it over the years. It's one I keep and revisit as the concepts take time to be fully grasped or integrated. If you can put aside (if you have a problem with it), the idea that all of the information is channeled to Esther Hicks by an "entity" named Abraham there is much to learn. It doesn't matter if you think that's weird or even if you think it's "wrong" somehow. Put judgement aside and see what is applicable here for your life.
Your second point is an interesting discussion. You are correct that in its infancy, psychology was criticized for claiming to be a scientific field and not living up to that assertion by performing quality research. I believe that this question has been put to rest as the rigors of publishing in psychology require randomized, double-blind, placebo controlled trials.
But the one who really first articulated the Law as general principle was Prentice Mulford. Mulford, a pivotal figure in the development of New Thought thinking, discusses the Law of Attraction at length in, for example, his essay "The Law of Success", published 1886-1887. In this, Mulford was followed by other New Thought authors, such as Henry Wood (starting with his God’s Image in Man, 1892), and Ralph Waldo Trine (starting with his first book, What All the World's A-Seeking, 1896). For these authors, the Law of Attraction is concerned not only about health but every aspect of life.
Many people turn to a greater power to help them increase their luck. Some say a prayer before they start to enter sweepstakes, asking God to help them win what they need or to help the prize go to the person who needs it most. Others feel that asking God for specific prizes is inappropriate but ask instead for the strength and the positive attitude they need not give up and to keep entering sweepstakes.
The law of attraction is not a magic wand. Because the brain preferentially scans and stores negative experiences, we have to consciously, habitually build the positive mental muscle. We all have layers and layers of stories, limiting beliefs, fears and blocks that have become the interior landscape of our minds and cannot be changed overnight just by thinking positive thoughts.
Visualize. Visualizing is an effective tool when it comes to attracting good luck and fortune. When you picture yourself experiencing a desired outcome, you work out the steps to overcome any obstacles. It motivates you toward your goals and gives you energy to take action. It can also give you new ideas and new ways to achieve your goals. For instance: If you want to be a successful singer, visualize yourself as one. Imagine yourself singing at a concert with fans all around you. It will raise your confidence. If you find visualizing things difficult, practice it. Close your eyes and try to see it in detail in your mind.
Before you begin to embark on the incredible journey towards true enlightenment in the Law of Attraction, it is important that you understand that you can apply it to your life and it can be effective if the correct tools are used. The practices and beliefs in this law have been igniting the lives of great individuals throughout the course of history.