If you havent modified the litium accelerator orderstatebuilder then you really only need to set deliverystate to delivered and that will trigger the rest.
Delivery state delivered will trigger capturepayment and trigger paymentstate move to paid and that in turn will trigger orderstate to go to completed if delivery state = delivered and paymentstate paid.
In the default implementation of the accelerator these states are related but if you have a customer orderflow you might have to add cinfguration for the related states.