s3 bucket life cycle management question

There is no fee for the life cycle rule itself.
https://docs.aws.amazon.com/AmazonS3/latest/userguide/how-to-set-lifecycle-configuration-intro.html

There may be a lag between when the Lifecycle configuration rules are satisfied and when the action triggered by satisfying the rule is taken. However, changes in billing happen as soon as the Lifecycle configuration rule is satisfied, even if the action is not yet taken.

For example, after the object expiration time, you are not charged for storage, even if the object is not deleted immediately. Another example, as soon as the object transition time elapses, you are charged S3 Glacier Flexible Retrieval storage rates, even if the object is not immediately transitioned to the S3 Glacier Flexible Retrieval storage class. Lifecycle transitions to the S3 Intelligent-Tiering storage class are the exception. Changes in billing do not happen until the object has transitioned into the S3 Intelligent-Tiering storage class.

However, there may be a charge for requests generated by lifecycle rules (e.g., storage class migration).
In your case, it should be considered a deletion, so there would be no fee.
https://aws.amazon.com/s3/pricing/?nc1=h_ls

DELETE and CANCEL requests are free.