首先，需要确保安装了AWS CLI和CDK。然后，可以按照以下步骤解决问题：

1. 在本地创建AspNetCore应用并测试

var builder = WebApplication.CreateBuilder(args);

builder.Services.AddControllers();
builder.Services.AddSwaggerGen(c =>
{
    c.SwaggerDoc("v1", new() { Title = "TestMinimalApi", Version = "v1" });
});

var app = builder.Build();

app.UseSwagger();

app.UseSwaggerUI(c => c.SwaggerEndpoint("/swagger/v1/swagger.json", "TestMinimalApi v1"));

app.MapControllers();

app.Run();

2. 安装AWS Lambda和Amazon.Lambda.Tools NuGet包。可以使用以下命令行：

dotnet tool install -g Amazon.Lambda.Tools

3. 要使用CDK进行Lambda部署，请执行以下命令行：

var app = new App();

var stack = new Stack(app, "StackName", new StackProps
{
    Env = new Environment
    {
        Account = "123456789012",
        Region = "us-west-2",
    },
});

var appFunction = new DotNetCoreFunction(stack, "FunctionName", new DotNetCoreFunctionProps
{
    Runtime = Runtime.DOTNET_CORE_3_1,
    Code = Code.FromAsset("path/to/project.zip"),
    Handler = "TestMinimalApi::TestMinimalApi.LambdaEntryPoint::FunctionHandlerAsync",
});

appFunction.AddEnvironment("ASPNETCORE_ENVIRONMENT", "Development");
appFunction.AddEnvironment("AWS_LAMBDA_LOGGER_LOGGERHANDLER", "Amazon.Lambda.Logging.AspNetCoreLogging.AspNetCoreLogProvider::Initialize");

new CfnOutput(stack, "FunctionArn", new CfnOutputProps
{
    Value = appFunction.FunctionArn,
});

app.Synth();

4. 在AWS Lambda控制台上创建一个新的Lambda函数，并将刚刚合成的CDK代码推送到该Lambda函数。

5. 在本地测试应用并确认是否正常运行。

通过以上步骤，可以成功地使用CDK将Asp.Net Minimal API（顶级语句）部署到Lambda上。