As with "quickening" yet another vague term used by Calvinism is "eyes opened." Many, many passages use this phrase to describe folks who were actually blind, and by a creative miracle were given sight.
But the phrase, and similar phrases, are used to describe someone given a "new insight" or an understanding, that they did not have before. Adam and Eve, after they ate the fruit of the tree, now could "see" they were naked, their eyes were opened so to speak, but what is really being said is they looked at something in a different light, they comprehended something they had not comprehended before, Genesis 3:5-7.
In 1 John 5:20 we see that Christ's revelation of God gives understanding. In the same way, Paul's words describing our Lord, Jesus Christ, opened the heart of Lydia, and she responded to the message.
Romans 9:16 teaches salvation does not depend on the man that wills, which teaches men will but salvation does not depend on their willingness, rather it depends on God. Putting our trust in Christ does not save us, but God crediting our faith in Christ as righteousness does save us.
Calvinism wrongly asserts natural men in an unregenerate - spiritually dead - state cannot will to be saved, but 1 Corinthians 2:14-3:3 teaches the opposite, natural men, like babes in Christ can understand the milk of the gospel, but cannot understand "solid food." So natural men are unable to understand "some" spiritual things, but not "all" spiritual things. But, and this is key, some spiritual things includes the milk of the gospel; the very one Lydia responded to.