In your scenario, it is not a tax-free payment and the employer is not using the CARES provision correctly, it is simply a taxable bonus that is included on your W-2 and you pay tax on. In that case, since you paid your loans with after-tax money, you can use the student loan interest deduction. But that scenario does not use the LRAP provisions of the CARES act.
There are two typical ways that an LRAP can be applied, as far as I can see.
For employees in certain public service jobs, the employer provides a loan to the employee that is used to pay the student loan payments. If the employee meets the employment conditions, the loan is forgiven by the employer and the forgiven loan is not counted as taxable income (as forgiven loans usually are).
For employees not in qualified public service jobs, the employer makes a payment directly to the lender. The value of those payments is added to the employee's W-2 as taxable income, and since it is taxable, the employee can use the student loan interest deduction.
The CARES act makes employer loan assistance paid from March 27 through December 31, 2020, a tax-free employee benefit up to $5250 (combined maximum for tuition assistance and loan assistance). The payment does not have to be directly to the lender, but the employer does have to follow all the normal rules for educational assistance plans (such as, they must have a written plan, must notify all eligible employees of the existence of the benefit, and must offer the fringe benefit to all eligible employees).
Assuming your employer has, or creates, an educational assistance plan that covers employee tuition and/or student loan payments, that is fair and complies with all the rules and regulations for employee educational assistance plans, then any payments made to you for the payment of your loans would not be included in your W-2 taxable wages and would not be counted toward social security or retirement match. Then, you can't deduct any part of your student loan interest that was paid with tax-free assistance. (For example, if you paid $500 per month in student loan payments ($6000 per year), and $5250 was tax-free assistance, then you could only deduct 12.5% of your interest for the year.)
If your employer does not already have an educational assistance program, they may want to work with a fringe benefit specialist or consultant to set up a program that conforms to the proper rules and regulations, so you and the employer don't get hit with unexpected penalties.
