A Boeing 747 was being radar vectored for Melbourne runway 34 when radar controllers noticed an unidentified aircraft at 2,400 ft in controlled airspace (CTA) where it should not have been above 1,500 ft outside controlled airspace. The departures south controller immediately instructed the Boeing 747 pilot to turn right 60 degrees due to conflicting traffic. Melbourne radar advisory service (RAS) gave a general broadcast to any aircraft heading up the western lane to descend immediately to 1,500 ft, but there was no response. Both aircraft passed within approximately 1 mile and 700 ft. With advice from Essendon Tower, RAS identified the offending aircraft near Brooklyn as VH-LOR and instructed the pilot to descend to 1,500 ft. About 5 minutes later, 2 miles west of Mount Cottrell, LOR climbed above 2,500 ft into CTA without a clearance and was again corrected by RAS. A student pilot was flying LOR on his second solo navigational exercise. He subsequently advised that he must have made errors in navigation because each time he inadvertently penetrated CTA he thought he was much further west where the base of the CTA was higher. The student pilot was required to undergo more dual instruction before the next solo navigational flight.