If I plan to pay off the mortgage with a lump sum, am I eligible for any discount?

No. You may be able to negotiate with the lender for a lower payoff, but that's unlikely. Remember though you pay off the PRINCIPAL balance. You don't pay any unaccrued interest.

On the other hand, you need to look at the tax implications here. You are losing a tax deduction as well as the potential income on the money used to payoff the balance. Depending on the interest rate on the mortgage, it may not make sense to do this payoff.