I means that, as far as I can tell, Lydia was not just another Gentile woman.
She was, in all likelihood, a descendant of Israel.
Baptism would have been a logical step.
I'm not entirely sure, though, if I were to hazard a guess, Paul's gospel.
I would argue that there simply isn't enough information to say definitively either way, since baptism is technically a part of both the Kingdom gospel and Paul's gospel of grace, just that they're different kinds of baptism.
If she was saved under the latter, then (as far as the English translation is concerned) there's enough leeway in the text for it to be either baptism by water (since they were literally standing next to a river, as shown by the photo in the above video), or given that it was Paul, baptism into the Body of Christ with no water needed, which Paul does describe as part of the process (and which the text does not necessarily exclude) of "being saved":
Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death? Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life.
Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death? Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life.
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For as the body is one and has many members, but all the members of that one body, being many, are one body, so also is Christ. For by one Spirit we were all baptized into one body—whether Jews or Greeks, whether slaves or free—and have all been made to drink into one Spirit. For in fact the body is not one member but many.
Unity and Diversity in One Body - For as the body is one and has many members, but all the members of that one body, being many, are one body, so also is Christ. For by one Spirit we were all baptized into one body—whether Jews or Greeks, whether slaves or free—and have all been made to drink...
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For you are all sons of God through faith in Christ Jesus. For as many of you as were baptized into Christ have put on Christ. There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus. And if you are Christ’s, then you are Abraham’s seed, and heirs according to the promise.
Sons and Heirs - For you are all sons of God through faith in Christ Jesus. For as many of you as were baptized into Christ have put on Christ. There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus. And if you are...
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There is one body and one Spirit, just as you were called in one hope of your calling; one Lord, one faith, one baptism; one God and Father of all, who is above all, and through all, and in you all.
There is one body and one Spirit, just as you were called in one hope of your calling; one Lord, one faith, one baptism; one God and Father of all, who is above all, and through all, and in you all.
www.biblegateway.com
In Him you were also circumcised with the circumcision made without hands, by putting off the body of the sins of the flesh, by the circumcision of Christ, buried with Him in baptism, in which you also were raised with Him through faith in the working of God, who raised Him from the dead. And you, being dead in your trespasses and the uncircumcision of your flesh, He has made alive together with Him, having forgiven you all trespasses, having wiped out the handwriting of requirements that was against us, which was contrary to us. And He has taken it out of the way, having nailed it to the cross. Having disarmed principalities and powers, He made a public spectacle of them, triumphing over them in it. So let no one judge you in food or in drink, or regarding a festival or a new moon or sabbaths, which are a shadow of things to come, but the substance is of Christ. Let no one cheat you of your reward, taking delight in false humility and worship of angels, intruding into those things which he has not seen, vainly puffed up by his fleshly mind, and not holding fast to the Head, from whom all the body, nourished and knit together by joints and ligaments, grows with the increase that is from God. Therefore, if you died with Christ from the basic principles of the world, why, as though living in the world, do you subject yourselves to regulations— “Do not touch, do not taste, do not handle,” which all concern things which perish with the using—according to the commandments and doctrines of men? These things indeed have an appearance of wisdom in self-imposed religion, false humility, and neglect of the body, but are of no value against the indulgence of the flesh.
Not Legalism but Christ - In Him you were also circumcised with the circumcision made without hands, by putting off the body of the sins of the flesh, by the circumcision of Christ, buried with Him in baptism, in which you also were raised with Him through faith in the working of God, who raised...
www.biblegateway.com
One more thing to point out: Lydia was baptized on a Sabbath, praying with the other women present (the word used for "place of prayer" (G4335 proseuchen) is, specifically, as defined by Strong's, one "used by Jews, perhaps when there was no synagogue"), and worshipping God.
On the other hand, if it was the Gospel of the Kingdom of Israel, then there is certainly evidence for that, too, as 1) there was water present, 2) she, along with the other women present, was a Jewess, or at least of Hebrew descent, and 3) it was a Sabbath (which would be odd to mention if she was a Gentile).
Thoughts: I wonder if it was an anti-type of Peter's baptising of Cornelius, who was (as far as I could tell, but am willing to be shown to be wrong, or maybe I'm forgetting my stance that he was saved by grace?) baptized under the gospel of the Kingdom of Israel by Peter after he was told that the Gentiles had been made clean.