It depends on the complexity of your use case.
In a simple use case, we have a database column updated by multiple consumers for each stage in an Order lifecycle. This is done by a web service calling into the database.
The simple lifecycle goes from ACKNOWLEDGED > ACCEPTED/REJECTED > FULFILLED > CLOSED. All of these are in the same table on the same column. This is executed in java classes with no workflow.
A workflow engine is suited in a more complex use case which involves actions on multiple data providers eg: database or Content Mgmt or Document Mgmt or search engine, multiple parallel processes, forking based on the success/failure of a previous step, sending an email at a certain step, offline error alerting.
You can look at Apache ODE to implement this.