What is the ruling of Islamic law on the permissibility of a monthly salary earned from working for someone who does not pray? Is it considered lawful or not?

If the company's field of work is permissible, then your salary for your legitimate work is halal (permissible), and the employer's lack of prayer does not affect the permissibility of what you receive. However, if the company's field of work is forbidden, then it is not permissible for you to work there, and what you receive from it would be unlawful money because it results from an illegitimate activity.