Hi there. If I'm not mistaken, the Hebrew word that gets translated as 'evil' in this verse is רָע(ra') which throughout the Bible takes on many different meanings(e.g. when used as an adjective it could mean bad, disagreeable, unpleasant, low of value, grievous, etc, but when used as a noun[like in Isaiah 45:7], it could mean adversity[which isn't immoral in and of itself, especially if we{or God} are opposing evil], evil[the concept of it], misery, unhappiness, severity, and finally, the antithesis of peace; calamity or misfortune.
Those two words that I emboldened(grievous and severity) I am about to show you.
Proverbs 15:10(NASB) Grievous punishment is for him who forsakes the way; He who hates reproof will die.
Proverbs 15:10(KJV) Correction is grievous unto him that forsaketh the way: and he that hateth reproof shall die.
In this case, רָע is used to describe the heaviness we perceive when we are punished for our rebelling(in this case forsak[ing] the way)
Ezekiel 14:21(NASB) For thus says the Lord GOD, "How much more when I send My four severe judgments against Jerusalem: sword, famine, wild beasts and plague to cut off man and beast from it!
Ezekiel 14:21(KJV) For thus saith the Lord GOD; How much more when I send my four sore judgments upon Jerusalem, the sword, and the famine, and the noisome beast, and the pestilence, to cut off from it man and beast?
Here, רָע is being translated as severe when describing God's punishment for idolatry(this is understood when we read Ezekiel 14 from the beginning)
Finally, in this verse's case, רָע is best understood as calamity or misfortune and maybe adversity(like I said earlier, adversity, in and of itself, is not morally wrong since we read that God opposes the wicked and humbles the proud for right reasons).
So now, how should Isaiah 45:7 be interpreted? Let's begin at verse 1 "Thus says the Lord to Cyrus His anointed..."
Isaiah is assumed to have lived around 700 BC, the Cyrus that God is speaking about here is the same Cyrus who would allow the Jews to return to Jerusalem with Zerubbabel(we read this in Ezra 1-6). This happened in the late 6th century BC, more than a century after Isaiah 45.
So we are dealing with a prophecy here.
Now, vrs 2 and 3 describe what God will do for Cyrus(He will ensure Cyrus' Persian Empire is successful)
Verse 4 tells us why God is doing this(so that the Jews who were in exile under Cyrus could return to Jerusalem to rebuild the temple)
Verses 5 and 6, God further explains His purpose for bringing Cyrus to power(so that the world may be in awe of God and glorify Him)
And finally verse 7, God pretty much answers the question that is raised by the preceding 6 verses(i.e. "How can You accomplish this?"). God is Sovereign and in control over all of Creation. If His will is to redeem His people from exile, even though they were warned of this before it happened, then He will do everything within His power and according to Nature to accomplish this feat.
And because God is Holy(you quoted Lamentations 3:37,38 which is good because it tells us how God is incapable of committing any immoral act. Because of His nature, everything He does is good) we can be certain that in Isaiah 45:7(KJV), evil is meant to be understood as the opposite of peace(adversity, calamity, and misfortune, which are all different ways of God judging the wicked, much like a good earthly judge punishing criminals for their crimes). To further solidify this conclusion, look at how Isaiah 45:7 is structured. It deals with opposites. Light and Darkness. Peace and Evil(misfortune). It would be as if God said "I have created the heavens and the earth, the sun and the moon, man and woman, Jew and Gentile, etc).
I hope that helps.
Edit: By the way, this is my first post so sorry for the inconsistencies with the font and size. I didn't know what was happening when I was typing. All I knew was, once I inserted the Hebrew letters, the text just changed all of a sudden.