1. 确认PostgreSQL数据库是否正确配置，数据库地址、用户名、密码、端口是否正确。
2. 确认Lambda函数是否有足够的权限访问PostgreSQL数据库，可以使用以下代码为Lambda函数添加访问权限：

using Amazon.Lambda.Core;
using Amazon.Lambda.Serialization.SystemTextJson;
using Amazon.Lambda.SQSEvents;
using Npgsql;

[assembly: LambdaSerializer(typeof(DefaultLambdaJsonSerializer))]

namespace MyLambdaFunction
{
    public class Function
    {
        public void FunctionHandler(SQSEvent evnt, ILambdaContext context)
        {
            var connString = "Server=myServerAddress;Port=12345;Database=myDataBase;User Id=myUsername;Password=myPassword;";

            using var conn = new NpgsqlConnection(connString);
            conn.Open();

            using var cmd = new NpgsqlCommand
            {
                Connection = conn,
                CommandText = "SELECT version()"
            };

            using var reader = cmd.ExecuteReader();
            reader.Read();

            context.Logger.LogLine(reader.GetString(0));
        }
    }
}

3. 确认Lambda函数是否正确配置Serilog，尤其是PostgreSQL sink相关的配置项是否正确配置。可以使用以下代码示例进行配置：

using Amazon.Lambda.Core;
using Serilog;
using Serilog.Core;
using Serilog.Sinks.PostgreSQL;

[assembly: LambdaSerializer(typeof(Amazon.Lambda.Serialization.SystemTextJson.DefaultLambdaJsonSerializer))]

namespace MyLambdaFunction
{
    public class Function
    {
        private static Logger _logger;

        static Function()
        {
            _logger = new LoggerConfiguration()
                .WriteTo.PostgreSQL("Host=myServerAddress;Port=12345;Database=myDataBase;Username=myUsername;Password=myPassword;",
                    tableName: "Logs",
                    needAutoCreateTable: true)
                .CreateLogger();

            Log.Logger = _logger;
        }

        public void FunctionHandler()
        {
            Log.Information("Hello, world!");
        }
    }
}

以上代码仅供参考，确保根据实际情况修改配置项。同时，可以使用Serilog的自动配置进行配置，使用以下