diff --git a/packages/aws-cdk/lib/api/evaluate-cloudformation-template.ts b/packages/aws-cdk/lib/api/evaluate-cloudformation-template.ts
index 8d56646852d10..7a1238797e193 100644
--- a/packages/aws-cdk/lib/api/evaluate-cloudformation-template.ts
+++ b/packages/aws-cdk/lib/api/evaluate-cloudformation-template.ts
@@ -35,7 +35,7 @@ export class LazyListStackResources implements ListStackResources {
 }
 
 export interface LookupExport {
-  lookupExport(name: string): Promise<AWS.CloudFormation.Export>;
+  lookupExport(name: string): Promise<AWS.CloudFormation.Export | undefined>;
 }
 
 export class LookupExportError extends Error { }
@@ -45,7 +45,7 @@ export class LazyLookupExport implements LookupExport {
 
   constructor(private readonly sdk: ISDK) { }
 
-  async lookupExport(name: string): Promise<AWS.CloudFormation.Export> {
+  async lookupExport(name: string): Promise<AWS.CloudFormation.Export | undefined> {
     if (this.exports[name]) {
       return this.exports[name];
     }
@@ -63,7 +63,7 @@ export class LazyLookupExport implements LookupExport {
       }
     }
 
-    throw new LookupExportError(`CloudFormation Export cannot be resolved as it does not exist: ${name}`);
+    return undefined; // export not found
   }
 
   private async * listExports() {
@@ -253,6 +253,9 @@ export class EvaluateCloudFormationTemplate {
 
       async 'Fn::ImportValue'(name: string): Promise<string> {
         const exported = await self.lookupExport.lookupExport(name);
+        if (!exported) {
+          throw new CfnEvaluationException(`Export '${name}' could not be found for evaluation`);
+        }
         if (!exported.Value) {
           throw new CfnEvaluationException(`Export '${name}' exists without a value`);
         }
diff --git a/packages/aws-cdk/test/api/evaluate-cloudformation-template.test.ts b/packages/aws-cdk/test/api/evaluate-cloudformation-template.test.ts
index eeb022c219bac..576bab1853ca1 100644
--- a/packages/aws-cdk/test/api/evaluate-cloudformation-template.test.ts
+++ b/packages/aws-cdk/test/api/evaluate-cloudformation-template.test.ts
@@ -1,4 +1,5 @@
 import {
+  CfnEvaluationException,
   EvaluateCloudFormationTemplate,
   LazyListStackResources,
   LazyLookupExport,
@@ -106,8 +107,7 @@ describe('evaluateCfnExpression', () => {
       const evaluate = () => evaluateCfnTemplate.evaluateCfnExpression({
         'Fn::ImportValue': 'blah',
       });
-
-      await expect(evaluate).rejects.toBeInstanceOf(LookupExportError);
+      await expect(evaluate).rejects.toBeInstanceOf(CfnEvaluationException);
     });
   });
 });
diff --git a/packages/aws-cdk/test/api/lazy-lookup-export.test.ts b/packages/aws-cdk/test/api/lazy-lookup-export.test.ts
index d24cbcc81d965..9c00a2f855599 100644
--- a/packages/aws-cdk/test/api/lazy-lookup-export.test.ts
+++ b/packages/aws-cdk/test/api/lazy-lookup-export.test.ts
@@ -49,8 +49,8 @@ describe('LazyLookupExport', () => {
     it('returns the matching export', async () => {
       const name = 'test-name-3';
       const result = await lookup.lookupExport(name);
-      expect(result.Name).toEqual(name);
-      expect(result.Value).toEqual('test-value-3');
+      expect(result?.Name).toEqual(name);
+      expect(result?.Value).toEqual('test-value-3');
     });
 
     it('stops fetching once export is found', async () => {
@@ -76,8 +76,9 @@ describe('LazyLookupExport', () => {
       expect(listExports).toHaveBeenCalledTimes(1);
     });
 
-    it('throws if the export does not exist', async () => {
-      await expect(() => lookup.lookupExport('test-name-unknown')).rejects.toBeInstanceOf(LookupExportError);
+    it('returns undefined if the export does not exist', async () => {
+      const result = await lookup.lookupExport('test-name-unknown');
+      expect(result).toBeUndefined();
     });
   });
 });