For unemployment insurance purposes, Lack of work is code for "we didn't want to continue to employ this person, but we do not object to her being approved to draw unemployment benefits."
So they were being kind to you. Go file for unemployment insurance benefits immediately. Tell the system you were laid off due to lack of work. There is no appeal, there is no objection to lack of work, because that means you were let go at the discretion of the employer, and there is no protest from them against your being able to draw unemployment benefits.
If you have been working for a covered employer for the last 18 months at least, and have enough wages in the base period to set up a claim, you will be able to draw a weekly benefit until you find something else. Your past employer is saying the reason you are no longer working for them is by their choice, not because of something you did wrong. You do not know the whole economic situation of their business, they may have had issues that forced them to let someone go. What if they closed the whole business down? All the employees would be laid off due to lack of work in that case.
To protest and complain about a lack of work lay off is not indicative that you have been in the workforce very long or that you have much understanding about your rights and legal situation as an employee. In an "at will" state such as yours, any employee can be fired at any time for any reason. No you cannot file a grievance against it or sue somebody.
Only if you have proof you were mistreated on the job or were terminated (not usually the same as "laid off") due to being in an EEOC protected category would you have any sort of EEOC complaint. All sorts of employees are laid off by the hundreds from all sorts of businesses every day. This is not the same as being fired for cause, which you weren't.
