Short answer
– From a mainstream evangelical perspective, Isaiah 55:8–9 is written by the prophet Isaiah (Isaiah son of Amoz), the eighth‑century BC prophet who ministered in Judah in the days of Uzziah, Jotham, Ahaz and Hezekiah. Evangelicals generally treat Isaiah as the inspired human author of the book and understand these verses as part of Isaiah’s prophetic teaching about God’s sovereign wisdom and mercy.

Who Isaiah was (evangelical summary)
– Name and period: Isaiah, son of Amoz, an 8th‑century BC prophet centered in Jerusalem (usually dated ca. 740–680 BC).
– Ministry context: He prophesied during the reigns of several Judean kings and addressed both calls to repentance and promises of future restoration and blessing. His ministry included confrontation of social and religious unfaithfulness, warnings of judgment, and messianic hope.
– Personal details: The book reports Isaiah’s temple vision (Isaiah 6), symbolic family details (children with prophetic names) and his role as a public prophetic spokesman for God.
– Evangelical commitment: Evangelicals typically affirm Isaiah’s historical authorship and the book’s unity because they regard the Bible as divinely inspired and because the New Testament and Jewish tradition consistently cite Isaiah as a single prophetic author.

Why evangelicals accept Isaiah as author of chapter 55
– Internal witness: The book itself presents Isaiah as the prophet (Isaiah 1:1; Isaiah 6).
– Early reception: Jewish and Christian communities treated Isaiah as a canonical prophetic book attributed to Isaiah.
– Theological coherence: Many conservative scholars argue the themes and theology of the whole book (God’s holiness, judgment, mercy, the servant motif, messianic hope) form a coherent prophetic message that fits Isaiah’s life and calling.
– Predictive prophecy: Evangelicals are willing to read prophetic material as genuine foretelling (not merely hindsight), so the exilic or post‑exilic material in chapters 40–55 can be seen as Isaiah’s predictive prophecy.

A brief exegesis of Isaiah 55:8–9 (evangelical emphasis)
– The verses (KJV): “For my thoughts are not your thoughts, neither are your ways my ways, saith the Lord. For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts.”
– Meaning: These words stress God’s transcendence, wisdom and sovereignty: human perspective is limited and finite; God’s purposes and methods exceed human understanding. In chapter 55 the contrast serves to encourage trust in God’s gracious plans (the invitation to feast on God’s provision and to receive his pardon) even when those plans differ from human expectation.
– Theological implication: God’s higher “ways” include his purposes of mercy and salvation (culminating in Christ, from an evangelical viewpoint). Believers are called to repent, trust, and submit to God’s revealed will even when it surpasses human reasoning.
– Pastoral application: The passage comforts believers who face confusion, apparent failure, or unanswered questions—God knows more and works for ultimate good according to his purposes, so we rely on his wisdom by faith.

If you want
– I can point to evangelical commentaries and sermons on Isaiah 55 (e.g., J. A. Motyer’s The Prophecy of Isaiah, Derek Kidner’s Tyndale commentary on Isaiah, John N. Oswalt’s Isaiah volumes) or provide a short devotional reflection or sermon outline applying Isaiah 55:8–9. Which would you prefer?