Can I claim the LLC credit if I get Tuition Reimbursement from my employee?

It depends on the amount and whether you paid taxes on the reimbursement.

In general, your employer can reimburse you for higher education expenses and deduct up to $5,250 per employee per year as a business expense.

The first $5,250 is not included in your taxable income and you can't claim the Lifetime Learning Credit for it because you didn't pay it, or pay taxes on it.

If your tuition for the year is more than $5,250, your employer is required to report the amount above $5,250 as taxable income and include it on your W-2, unless the amount was excluded as a fringe benefit. 

The amount that was taxable income to you can be used to claim the Lifetime Learning Credit.

If you believe an amount was taxable to you, please verify this with your employer because in some cases the excess education expense can be considered a fringe benefit and is not included in your taxable income.