Art and music have been two of the guiding principals in Leitch's life. He worked for a time as a professional musician before committing fully to a career as a painter. The son of Christchurch based artist, Peter Leitch, Lawrence attended Wellington Polytechnic School of Design and on completion of his studies worked as a commercial artist. In the late 1980s Leitch spent time in the United States. Returning to New Zealand he became further involved in seriograph printmaking. In 1995 he was awarded a Gold Medal at the 1995 New Zealand Pride in Print Awards.

Leitch initially chose the medium of watercolour for his finely tuned realism. Subject matter was always the New Zealand landscape, predominantly regions of Central Otago, Coromandel and Auckland. In 2001 the artist began working on dramatic large scale acrylics. These spectacular works have enjoyed worldwide patronage and appreciation. There is a consistency in Leitch's work in that the human element is sometimes suggested but never portrayed, nature, rather than man, rules supreme and usually undisturbed. It is a tribute to the artist's versatility that he is able to capture the extreme contrasts of both the North and South Islands. Leitch's solo 2004 exhibition was a sellout.