Is it unethical if I did not inform the current lab I am in that I am looking for another position?
Generally speaking, no, you can seek other employment at any time without ethical constraint. This is especially true if the work environment is abusive in any way. 

There is one consideration, however, that you should keep in mind. If other people depend on your work, you need to do what you can so that you don't unnecessarily disadvantage them. So, you may have an obligation to complete joint work before you actually leave, or see that it is put into a proper state. But you don't have to do that first.