There are two things to remember with respect to the scriptures, God's Sovereignty and Man's Free Will, both which are BOTH vital to hold onto for a balanced view of the Scriptures.
Many a man cringes at the sovereignty that God has over his creation, namely complete and total control of everything he has made. He can control the weather of the earth, set the stars in motion etc. He is also higher than man and all the hosts of heaven, having authority over man, not only individually, but also nations as a whole as Romans 9 points out:
"Romans 9:19 You will say to me then, "Why does He still find fault? For who resists His will?" 20On the contrary, who are you, O man, who answers back to God? The thing molded will not say to the molder, "Why did you make me like this," will it? 21Or does not the potter have a right over the clay, to make from the same lump one vessel for honorable use and another for common use?…"
See also my video on Romans 9 for more information on who Romans 9 refers to: https://www.youtube.com/watch?v=8zDpEHynuGE
The Psalms also tell us about how God's sovereignty works and what it entails, specifically Psalms 103
"Psalm 103:19 The Lord has established his throne in heaven,
and his kingdom rules over all.
20 Praise the Lord, you his angels,
you mighty ones who do his bidding,
who obey his word.
21 Praise the Lord, all his heavenly hosts,
you his servants who do his will.
22 Praise the Lord, all his works
everywhere in his dominion.
Praise the Lord, my soul."
Numerous places throughout scripture makes clear that man is to submit to Jesus as Lord, just as a slave is to submit to his master. Christians are slaves of Christ and are called to be his obedient servants and to do only what pleases him, regardless of the cost.
"Philippians 1:1 Paul and Timothy, servants of Christ Jesus,
To all God’s holy people in Christ Jesus at Philippi, together with the overseers and deacons[a]:
2 Grace and peace to you from God our Father and the Lord Jesus Christ."
"1 Corinthians 6:19 Do you not know that your bodies are temples of the Holy Spirit, who is in you, whom you have received from God? You are not your own; 20 you were bought at a price. Therefore honor God with your bodies."
If one is a slave of Christ, he is under Christ's dominion and sovereignty. Man is under God's sovereignty and it is something that man seeks to be free from. The atheist, be he passive or aggressive, will not acknowledge God, because that would dethrone him from his pedestal and he doesn't want to put God on his throne.
Man's Free Will
Due to the fall of man and being tainted by original sin, Man's free will has been affectively lost and only can be regained if man has been quickened. Once man has been quickened, he then has the choice to either go back into his sin, or allow the Holy Spirit to cleanse him and bring him out of original sin that has destroyed him. Man doesn't have a choice and cannot exercise free will until the quickening.
Such an example can be found in the case of Felix in the book of Acts:
"Acts 24:24 Several days later Felix came with his wife Drusilla, who was Jewish. He sent for Paul and listened to him as he spoke about faith in Christ Jesus. 25 As Paul talked about righteousness, self-control and the judgment to come, Felix was afraid and said, “That’s enough for now! You may leave. When I find it convenient, I will send for you.” 26 At the same time he was hoping that Paul would offer him a bribe, so he sent for him frequently and talked with him.
27 When two years had passed, Felix was succeeded by Porcius Festus, but because Felix wanted to grant a favor to the Jews, he left Paul in prison."
Felix came under a conviction, but he was not regenerated by the Holy Spirit and resisted the prompting of the Spirit. Does this mean that God is not in total control? No, It just simply means that he doesn't force a man or woman to believe. If God wanted to, he could and would change Felix's heart just like that and force him to submit to him, but he did not, and ALLOWED Felix to rebel, considering Felix, despite a quickening, would not respond to the power of the Spirit and thus was left in his sin as punishment.
God doesn't force man to believe, he allows man to make a choice, but again, the choice cannot be made by man unless he has been quickened.
This is not God's plan being thwarted as some individuals claim and is certainly not a case of God's grace being insufficient. See my article response to KeithTruth's Facebook comments to me: http://answering-judaism.blogspot.co.uk/2014/06/a-question-to-keithtruth-arminianism.html
Now we turn our attention to Lydia briefly:
"13 On the Sabbath we went outside the city gate to the river, where we expected to find a place of prayer. We sat down and began to speak to the women who had gathered there. 14 One of those listening was a woman from the city of Thyatira named Lydia, a dealer in purple cloth. She was a worshiper of God. The Lord opened her heart to respond to Paul’s message. 15 When she and the members of her household were baptized, she invited us to her home. “If you consider me a believer in the Lord,” she said, “come and stay at my house.” And she persuaded us."
God did have his way in opening Lydia's heart to Paul's message, but in the context, NOWHERE does the silence on Lydia's compliance with God suggest that God simply forced her to believe. God certainly opened the door via quickening and Lydia reciprocated. Lydia could make the choice to reject the Spirit's prompting but didn't and using this text as a proof text to refute free will is at best, an argument from silence.
Arminianism affirms both the sovereignty of God and the free will of man are valid.
Roger Olson states in his book "Arminian Theology: Myths and Realities":
"CLASSICAL Arminianism goes far beyond belief in general providence to include affirmation of God’s intimate and direct involvement in every event of nature and history. The only thing the Arminian view of God’s sovereignty necessarily excludes is God’s authorship of sin and evil. Faithful followers of Arminius have always believed that God governs the entire universe and all of history. Nothing at all can happen without God’s permission, and many things are specifically and directly controlled and caused by God. Even sin and evil do not escape God’s providential governance in classical Arminian theology. God permits and limits them without willing or causing them."
This book I would recommend if you want to know what Arminianism teaches, but also reading Arminius himself would be beneficial.
I am aware of certain issues regarding Olson raised to me by KeithTruth, but this would not impact the point he has made and if you have any concerns about Olson, don't hesitate to express them.
I would recommend also this article here: http://arminiantheologyblog.wordpress.com/2012/07/16/do-arminians-believe-in-the-sovereignty-of-god/
God DOES have sovereignty over all in Arminianism and anyone who claims otherwise is attacking a strawman.
If anyone says "if God was completely sovereign, I would never worship him.", then I would have a problem with that statement. But since I acknowledge that God is sovereign, so be it if he is completely sovereign.
Hope this brings deals with certain issues.