First，lifetime gift exemption is same as the estate tax exemption. https://smartasset.com/retirement/lifetime-gift-tax-exemption You have the total $11 mil per person, no matter you give away during your life time or bequest it after death. You just report 709 forms about your gift every time you give someone something. When you file estate tax the IRS addes up all your lifetime gifts and deduct them from your estate tax exemption.
Second, don't be stupid. If you gift the house to the child now, the cost basis goes with the gift so your child will pay capital gain tax on the gain from the time YOU bought the house to the time HE sold it. If the house is transfered to your child when you die, the cost basis of the house is reset to the value at your time youf death, and your child pays no capital gain tax if he sells immediately.
This is called step-up basis, google it.
