Lawry was born in the Melbourne suburb of Thornbury. He was given the names William Morris after the early Prime Minister of Australia, William Morris Hughes. His father Alfred played amateur cricket until the age of 51. Bill never saw his father play, who was aged 47 when Bill was born. Aged nine, he played competitive cricket for the first time with the Thornbury Presbyterian Church team. He spent three years there, as well as playing for Preston Technical School. When he was twelve, he entered Melbourne's district competition playing for Northcote's fourth team, working his way up to the First XI by the age of sixteen. At the time, he was apprenticed as a plumber and attending Preston Technical College. Lawry was selected for Victoria's Second XI at the age of seventeen. He made a duck against the South Australians and did not see any further action for the Seconds for the rest of the summer of 1954–55. The following season, Lawry was recalled to the Seconds and scored 183 against South Australia.

A few months before turning nineteen, Lawry made his debut for Victoria, against Western Australia at the Junction Oval in the 1955–56 season. He scored only three as the hosts took an innings victory and it was his only senior match of the season. He played in all but one of Victoria's matches in 1956–57, but had modest results. He passed fifty only twice, scoring 51 against Queensland in his fourth first-class match, and making 74 against South Australia two games later. He made only one and seven against arch-rivals New South Wales in a low-scoring match that ended in the first tie in Sheffield Shield competitions. He ended with only 248 runs at 20.66.

Lawry was dropped completely in 1957–58 and did not play a match for his state even though they were depleted with Test representatives overseas in South Africa. The left-hander stayed on the sidelines for the first half of the following season when the Test players returned. Recalled for Victoria's match against the touring English cricket team in 1958–59, he scored 24 and 22, failing to seize his opportunity against international opponents. He also bowled at first-class level for the first time, bowling two overs without success. However, he was retained in the team, and scored fifties in four of the remaining five innings of the season and ended with 361 runs at 60.16.

In 1959–60, the national team were away on an eight-Test tour of the Indian subcontinent, opening up opportunities for players in domestic cricket. Lawry played in all 10 of Victoria's inter-state matches. After starting the season with 70 and 50 not out against Western Australia, Lawry went into form slump and accumulated only 56 runs in his next six innings. He scored 85 and 33 and took his maiden first-class wicket in the next match against South Australia, but his form remained modest until the end of the season. He scored fifties in consecutive matches before registering his maiden first-class century, 127, against Western Australia, before scoring an unbeaten 38 in the second innings to see the Victorians to their target of 46. He ended with 666 runs at 44.40 for the season.

His batting form remained modest at the start of the 1960–61 season, scoring only 148 runs in the first seven innings of the summer.