Yes, in Louisiana an attorney can quit representing you if you fail to pay her on time.
Louisiana Rule of Professional Conduct 1.16(b)(5) states that:
"...a lawyer may withdraw from representing a client if... (5) the client fails substantially to fulfill an obligation to the lawyer regarding the lawyer’s services and has been given reasonable warning that the lawyer will withdraw unless the obligation is fulfilled"
Thus, the attorney would be within her rights to withdraw herself from your case if you do not honor your agreement with her to pay her on a certain schedule.
However, the attorney cannot take any action that would harm your interests in the pending case. She has a duty to protect your interests by giving you reasonable notice before she quits, giving you time to find a new lawyer before she stops, returning any documents you need, or refunding any amount that you paid upfront that she hasn't earned.
I hope this answers your question. Best of luck.
This is an incomplete answer written in response to the limited facts provided. It is intended as a courtesy to better inform the reader about his or her possible rights and potential courses of action; it is not intended as formally researched legal advice or as an agreement to enter into an attorney-client relationship.
Overall, the fee itself sounds reasonable. But you may want to explore the reasonableness of the fee. As to the fee shift to $150 per hour, that is very standard. Since your attorney is working partly on contingency, she wants to make sure she is compensated if you go elsewhere and cut off that opportunity for her to recover 30%
No attorney client relationship is created by virtue of this answer. Further, answers are for information only and should not be relied upon unless there has been a formal consultation. Many cases are fact specific and there is simply no way an attorney could possibly provide complete advice without all the relevant facts.