Answer: to rally emotional support for a unified country
Explanation: While you could interpret this excerpt as Lincoln thanking the deceased soldiers' families for their support, there is greater textual support for the last option, "to rally emotional support for a unified country". Lincoln says that the fallen shall not die in vain, going on to then rally those at the address saying that this nation will have a new birth of freedom. This is meant to honor the dead in battle, while still driving hope and faith for the rest of the populace.
