In this scenario it's the same situation except that you'll receive an interest rate that is higher, and this can result in higherprofits from interest. Thus the lender will be able to pay the closing costs. But, you'll have an interest rate that is higher.
In the majority of cases you should not choose the lender-paid closing cost because the majority of the time, you'll pay more than the amount that the lender was paid in closing costs over time. Take a look at the scenario again but this time with a lender-paid closing costs.