Acts 16:14 And a certain woman named Lydia, a seller of purple, of the city of Thyatira, which worshipped God, heard us: whose heart the Lord opened, that she attended unto the things which were spoken of Paul.
The Lord opened Lydia's heart so that she attended to the gospel message that Paul gave to her.
Acts 18:27 And when he was disposed to pass into Achaia, the brethren wrote, exhorting the disciples to receive him: who, when he was come, helped them much which had believed through grace:
Acts 18:27 βουλομένου δὲ αὐτοῦ διελθεῖν εἰς τὴν Ἀχαΐαν, προτρεψάμενοι οἱ ἀδελφοὶ ἔγραψαν τοῖς μαθηταῖς ἀποδέξασθαι αὐτόν· ὃς παραγενόμενος συνεβάλετο πολὺ τοῖς πεπιστευκόσι διὰ τῆς χάριτος·
The perfect active participle plus dia with grace in the genitive as its object proves that these people had believed through the grace that was given to them. Saving faith is always only by the grace (totally unmerited and unmeritable favor) that God bestows upon completely undeserving sinners.
In the first place, when you try to USE any Scripture to TRY and "prove" what you believe, you will do well to be honest and look at the WHOLE CONTEXT!
It is BECAUSE Lydia was ALREADY a "Worshiper" of the One True God, that is, a SEEKER of God, God sent Paul to speak the Gospel to her, and "opened her heart" so that she might comprehend what she was been told! Don't ADD to what the Bible clearly says!
This is EXACTLY what we read in chapter 10 of Acts, of the conversion of Cornelius.
BEFORE Peter went to preach the Gospel of salvation, this is what the Bible actually says;
"There was a man in Caesarea named Cornelius, a centurion of what was called the Italian Regiment.
He was a devout man and feared God along with his whole household.
He did many charitable deeds for the Jewish people and always prayed to God. About three in the afternoon he distinctly saw in a vision an angel of God who came in and said to him, “Cornelius!” Looking intently at him, he became afraid and said, “What is it, lord?” The angel told him, “
Your prayers and your acts of charity have come up as a memorial offering before God" verses 1-4
It is BECAUSE of Cornelius FEARING God with his household, and his PRAYERS to God, that was the REASON for God sending Peter with the Gospel.
Read also verses 34-35
"Then Peter began to speak: “Now I really understand that God doesn’t show favoritism, but in
every nation the person who fears Him and does righteousness is acceptable to Him"
EVERYONE who FEARS the God of the Bible, and
DOES RIGHTEOUSNESS, is ACCEPTABLE to God!
This does NOT mean that these are somehow automatically saved, but rather, that God will make sure that any TRUE SEEKER of Him WILL hear the Gospel"
As Paul tells us in Acts 17:27, "He did this so they might seek God, and perhaps they might
reach out and find Him, though He is not far from each one of us"
God does NOT bestow any "saving faith or grace" on only the so called "elect", as some erroneously teach!
"God LOVES VERY MUCH THE ENTIRE HUMAN RACE, with a SAVING LOVE, that ANYONE from this HUMAN RACE who truly BELIEVES, WILL be saved" (John 3:16, my translation)
ANY "limitations" on the extent of the Death of Jesus Christ, is RANK HERESY, and comes not from the God of the Bible; but the devil himself!