feat(lambda): add NodeJS 22.x support (aws#32104)

### Issue # (if applicable)

NA

### Reason for this change

Adds NodeJs 22.x Runtime to the available [Lambda Runtimes constants](https://docs.aws.amazon.com/cdk/api/v2/docs/aws-cdk-lib.aws_lambda.Runtime.html#initializer)

### Description of how you validated changes

Have added integration tests to validate the runtime support

### Checklist
- [ ] My code adheres to the [CONTRIBUTING GUIDE](https://github.com/aws/aws-cdk/blob/main/CONTRIBUTING.md) and [DESIGN GUIDELINES](https://github.com/aws/aws-cdk/blob/main/docs/DESIGN_GUIDELINES.md)

----

*By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license*

packages/@aws-cdk-testing/framework-integ/test/aws-lambda/test/integ.runtime.inlinecode.js.snapshot/aws-cdk-lambda-runtime-inlinecode.template.json

@@ -349,6 +349,56 @@
    "DependsOn": [
     "NODEJS20XServiceRole188A4E38"
    ]
+  },
+  "NODEJS22XServiceRole8FE2F7A5": {
+   "Type": "AWS::IAM::Role",
+   "Properties": {
+    "AssumeRolePolicyDocument": {
+     "Statement": [
+      {
+       "Action": "sts:AssumeRole",
+       "Effect": "Allow",
+       "Principal": {
+        "Service": "lambda.amazonaws.com"
+       }
+      }
+     ],
+     "Version": "2012-10-17"
+    },
+    "ManagedPolicyArns": [
+     {
+      "Fn::Join": [
+       "",
+       [
+        "arn:",
+        {
+         "Ref": "AWS::Partition"
+        },
+        ":iam::aws:policy/service-role/AWSLambdaBasicExecutionRole"
+       ]
+      ]
+     }
+    ]
+   }
+  },
+  "NODEJS22X911196A1": {
+   "Type": "AWS::Lambda::Function",
+   "Properties": {
+    "Code": {
+     "ZipFile": "exports.handler = async function(event) { return \"success\" }"
+    },
+    "Handler": "index.handler",
+    "Role": {
+     "Fn::GetAtt": [
+      "NODEJS22XServiceRole8FE2F7A5",
+      "Arn"
+     ]
+    },
+    "Runtime": "nodejs22.x"
+   },
+   "DependsOn": [
+    "NODEJS22XServiceRole8FE2F7A5"
+   ]
   }
  },
  "Outputs": {
@@ -386,6 +436,11 @@
    "Value": {
     "Ref": "NODEJS20X70A25ADE"
    }
+  },
+  "NODEJS22XfunctionName": {
+   "Value": {
+    "Ref": "NODEJS22X911196A1"
+   }
   }
  },
  "Parameters": {

packages/@aws-cdk-testing/framework-integ/test/aws-lambda/test/integ.runtime.inlinecode.ts

@@ -65,6 +65,13 @@ const node20xfn = new Function(stack, 'NODEJS_20_X', {
 });
 new CfnOutput(stack, 'NODEJS_20_X-functionName', { value: node20xfn.functionName });
 
+const node22xfn = new Function(stack, 'NODEJS_22_X', {
+  code: new InlineCode('exports.handler = async function(event) { return "success" }'),
+  handler: 'index.handler',
+  runtime: Runtime.NODEJS_22_X,
+});
+new CfnOutput(stack, 'NODEJS_22_X-functionName', { value: node22xfn.functionName });
+
 new integ.IntegTest(app, 'lambda-runtime-inlinecode', {
   testCases: [stack],
 });

packages/aws-cdk-lib/aws-lambda/lib/runtime.ts

@@ -118,6 +118,11 @@ export class Runtime {
    */
   public static readonly NODEJS_LATEST = new Runtime('nodejs18.x', RuntimeFamily.NODEJS, { supportsInlineCode: true, isVariable: true });
 
+  /**
+   * The NodeJS 22.x runtime (nodejs22.x)
+   */
+  public static readonly NODEJS_22_X = new Runtime('nodejs22.x', RuntimeFamily.NODEJS, { supportsInlineCode: true });
+
   /**
    * The Python 2.7 runtime (python2.7)
    * @deprecated Legacy runtime no longer supported by AWS Lambda. Migrate to the latest Python runtime.