It is known that AWS lambda may reuse early created objects of handlers, and it really does it (see FAQ):
Q: Will AWS Lambda reuse fu
Taking advantage of the execution context reuse is definitely a practice when working with AWS Lambda (See AWS Lambda Best Practices). But this does not apply to concurrent executions as for concurrent execution a new container is created and thus new context. In short, for concurrent executions if one handler changes the value other won't get the new value.