Not sure how “your lawyer” can refuse your case. An attorney does not have to take on a case, just like a doctor cannot be forced to treat a patient. If you signed a retainer with the attorney then that is another story and there could be legal reasons why he/she no longer wants to handle the matter.
DISCLAIMER: David J. McCormick is licensed to practice law in the State of Wisconsin and this answer is being provided for informational purposes only because the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship.
Report him to the bar for what? If someone offered you $10 to dig a ditch for them and you refused because it was not financially rewarding for you, would you be in the wrong?
Find another attorney and be willing to pay them their hourly fee to make it worthwhile, when you end up losing money on it, only blame yourself.
Every legal matter is fact specific, and there are often nuances in every case. This is intended for comment only, and does not create an attorney client relationship.
There is no ethical violation by refusing to take on a case. He may feel the case is without merit in that there is a lack of liability or an inability to prove damages. Certainly he can refuse. Go shop around if you feel you have a case.
Why would you report this lawyer for declining your case? He may decline the case.
If you believe you have a viable case, your time would be more productively spent talking to one of the many lawyers in the Austin area.