I was granted an Australian visa but lost the passport details were used to grant the visa and still validate of 4 years. Is it possible to travel with the new passport since it carries the passport number of the previous one that was lost?
Because some of your passport details will have changed, you should log in to ImmiAccount and update them, even if your passport number is the same (which seems unlikely but ok).
Australian visas which are electronically issued may be updated electronically, and you usually do not need to reapply for the visa when you get a new passport. AFAIK Australia is the only country which allows keeping the visa without reapplying in this scenario.
If you are not able to update your details in ImmiAccount, you can fill out the paper Form 929, but it takes a few weeks to update your information this way.
You may also check the validity of your visa.