Reconciling God's sovereignty even in evil is a difficult concept, but one that if pursued and appealed to the Spirit for understanding, makes all the difference. A few resources to get you on your way include reading Psalm 105 for a start. God He also turned the hearts of Egyptians to hate his people, and caused themto deal craftily with his servants. God did those things and more. On purpose.
Secondly, here is a great sermon on the subject,
"Genesis 20: How Does Sin Relate to God’s Sovereign Plan?"
Finally, here is a good article on the topic by Mike Riccardi.
Suffering Well: Recognizing the Enemy
Quite simply, a Bible-believing Christian has no choice but to admit that God sovereignly and actively brings about the evil events described in Lamentations. But if our understanding of God’s absolute sovereignty leads us to conclude that He is morally culpable, blameworthy, or in any way unrighteous, we’re wrong. The Scripture writers never seek to save God from His sovereignty in evil and sinful events, yet they also never attribute evil to Him directly.
God is orderly. He has a plan. (John Bunyan's Order and Causes of Salvation & Damnation)
