send filtered log message of Metric Filter to Lambda function

You cannot send logs to Lambda using a metrics filter.
Metrics filtering is a function that filters logs and counts necessary information as metric values.
https://docs.aws.amazon.com/AmazonCloudWatch/latest/logs/MonitoringLogData.html

You can search and filter the log data coming into CloudWatch Logs by creating one or more metric filters. Metric filters define the terms and patterns to look for in log data as it is sent to CloudWatch Logs. CloudWatch Logs uses these metric filters to turn log data into numerical CloudWatch metrics that you can graph or set an alarm on.

Use the subscription filter.
https://docs.aws.amazon.com/AmazonCloudWatch/latest/logs/SubscriptionFilters.html#LambdaFunctionExample