A tuition waiver for your spouse who is not an employee, must be included in your taxable income. The $5250 tax-free limit only applies to fringe benefits for employees, not the rest of their family.
Assuming that the spouse's tuition waiver will be included in your box 1 taxable wages of your W-2 for the year it was paid (2019 or 2020), then you are paying the tuition with taxable money, the same as if your employer gave you a raise, taxed it, and then you spent the money on tuition. As such, your spouse is eligible for the lifetime learning credit since the tuition was paid with after-tax funds.
