In some businesses, there clearly can be a conflict between an owner’s desire to pay employees a “living wage” and the owner's desire to profit as much as possible—or even profit at all. Not all employees in all industries are productive enough that their employers can afford to pay them a living wage.
In order for a business owner to pay an employee a given amount of money, the employee has to produce more revenue than that amount. For example, if a fast food employee wants to make $15 per hour, they have to produce more than $15 of revenue each hour. They need to produce more than $15 to pay for “their” share of the overhead costs and to provide some profit for the owner. In businesses like fast food, stores are often not able to generate enough revenue each hour to be able to pay at least a “living wage” (however that is defined) to each employee. These businesses are unable to charge high enough prices for their products to bring in enough revenue to pay such a wage.
In some industries, it is easy to pay everyone a living wage. There are many lines of work, however, in which employees simply do not contribute that much to the firm’s overall revenue. If a business owner pays a living wage to such an employee, the employer is essentially giving them money the employee has not earned. It is difficult for a business to be successful while paying people more than they are worth. For this reason, I do see at least a potential conflict between the desire to pay a living wage and the desire/ need to be profitable.