Was Lydia just accidentally in the right place at the right time?
No. Lydia was not merely accidentally in the right place at the right time. Although from her viewpoint it seemed accidental, nothing just happens when God is in the picture. It was a divine appointment, with the sovereign God behind it, opening her heart to hear Paul's word.
Les explains that Lydia's encounter was a divine appointment, not a random coincidence. Paul had come across from Asia Minor into Macedonia because the Spirit gave him the vision to go there. On the Sabbath, he went out by the riverside where prayer was customarily made and spoke to the women gathered there. Lydia, a seller of purple from Thyatira who worshipped God, heard Paul, and the Lord opened her heart. Had Paul not come to that particular riverside park on that particular Sabbath, she would never have heard the Word. From her point of view, she accidentally was in the right place at the right time, but always behind it is the sovereign God. Les applies the same principle to those who think they accidentally ran across his television program; it is not accidental, because the Lord is in it from start to finish.
And on the sabbath we went out of the city by a river side, where prayer was wont to be made; and we sat down, and spake unto the women which resorted thither.
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