"One who heard us was a woman named Lydia, from the city of Thyatira, a seller of purple goods, who was a worshiper of God. The Lord opened her heart to pay attention to what was said by Paul. And after she was baptized, and her household as well, she urged us, saying, ‘If you have judged me to be faithful to the Lord, come to my house and stay.’ And she prevailed upon us." (Acts 16:14-15; ESV)
Why was Lydia baptized? We know there was not a local church in Philippi. Paul and Silas are bringing Christianity for the first time into the Macedonian region. There were not even enough Jewish men in Philippi to establish a synagogue. Lydia could not have been baptized to join the local church because a local church did not exist. Nor could she have been baptized to witness to other believers that she was a Christian. There were no other Christians. Lydia and her household are the first converts in Philippi. If God knew Lydia was saved and Paul and Silas knew Lydia was saved, why was Lydia baptized? Isn’t this a pointless act? All of the explanations given today in the denominations for the purpose of baptism simply do not make sense concerning Lydia. She is not joining a local church nor is she making a statement to believers that she is already saved.
The most logical answer is that baptism was just as much of a requirement to receive the grace of God as belief, repentance, and confession. If baptism was not necessary, why was Lydia and her household baptized? Obviously, baptism was necessary. By being baptized, they were not relying upon themselves to be saved. No more than praying to God, repenting, and confessing is relying upon yourself for salvation. Baptism was simply another necessary step, like repentance and confession, to ask God to apply His grace and remove sins.
I do not have another logical explanation for Lydia and her household being baptized.