Not usually
You may only be dismissed in Australia for fair reason. These are:
- poor performance
- misconduct
- dangerous behaviour
- refusing to follow instructions
- no further need for the position (redundancy or retrenchment)
Refusing to do as you are told would fall under “refusing to follow instructions”. However, an “instruction” must be both lawful and reasonable. Depending on the lie, it might not be lawful or reasonable. If so, you can’t be fired at all.
If it is a lawful and reasonable instruction then there are not grounds to instantly fire someone.
Even when you have a reason, except for gross misconduct, you can’t dismiss an employee unless and until they have been given a fair hearing to explain themselves and have been given the opportunity to “med“mend their ways”. Even for gross misconduct, they still must be given an opportunity to justify their conduct.