Best practice to store single value in AWS Lambda

Use DynamoDB. There is no overhead for "running a database" -- it is a fully-managed service. You pay only for storage and provisioned capacity. It sounds like your use-case would fit within the Free Usage Tier.

Alternatively, you could use API Gateway with a cache setting so that it doesn't even call the Lambda function unless a timeout has passsed.

You could consider AWS Parameter Store

AWS Systems Manager Parameter Store provides secure, hierarchical storage for configuration data management and secrets management. You can store data such as passwords, database strings, and license codes as parameter values. You can store values as plain text or encrypted data. You can then reference values by using the unique name that you specified when you created the parameter. Highly scalable, available, and durable, Parameter Store is backed by the AWS Cloud. Parameter Store is offered at no additional charge.