There are situations in the Bible where God's laws seemingly conflict, such as what happens when someone is commanded to circumcise a baby boy on the 8th day and that happens to fall on the Sabbath. The issue is not that they obeyed one command and sinned by breaking the other, but rather that one of the commands was never intended to prohibit obeying the other. In other words, the command to keep the Sabbath was never intended to prohibit the command to circumcise on the 8th day, so they were not breaking the Sabbath by doing so. There can be similar situations when the command to love our neighbor can seemingly conflict with the command to not bear false witness, but I think the command to love our neighbor has priority, and the command to not bear false witness was never intended to prohibit us from loving our neighbor.