Sir Lance was born in Wellington, New Zealand to Arthur Archibald Adams and Hilda Mary Adams (nee Biggs). He was educated at Eastern Hutt Primary School, Petone Memorial Technical College, and Mount Albert Grammar School, Auckland. Sir Lance's mother died when he was three and his Aunt Susan (Susan Isabella Schneider nee Adams, one of Arthur's sisters) took on the care of her nephew. Later Susan and her husband, Theodore Schneider, were to adopt Lance and he became Lance Adams-Schneider.
Adams-Schneider entered the drapery trade on leaving school and founded his own business in Auckland. Later he managed a large store in Taumarunui. During the Second World War Sir Lance served in the Medical Corps. Later Lance became a member of the Taumarunui Borough Council, President of the Chamber of Commerce and Executive Member of the NZ Retailers’ Association.
Adams-Schneider stood in the Hutt electorate against Walter Nash in 1957, coming second for National. He then contested and won for National the 1959 Hamilton by-election held after the death of Dame Hilda Ross the MP for Hamilton. He continued to represent the Hamilton electorate until its disestablishment in 1969, after which he represented the Waikato electorate until his retirement in 1981.
Sir Lance was a parliamentary under-secretary from 1964 to 1967, Minister of Broadcasting from 1967 to 1969, Minister of Customs from 1969 to 1972, Minister of Health and Minister of Social Welfare in 1972, and Minister of Trade and Industry from 1975 to 1981.
In the 1984 Queen's Birthday Honours, Adams-Schneider was appointed a Knight Commander of the Order of St Michael and St George, (KCGM)for public services. He was also a member of the Honourable Privy Council.