Steve passed away Thursday as a result of complications from Alzheimer's disease ... this according to his son, David. He released a statement in the aftermath of his father's death -- saying, "My Dad was an inspiration to so many people. But, to me, he was just this charming, handsome, hysterically funny guy who sang a lot. Sometimes alone and sometimes with his insanely talented wife."

He added, "I am so lucky to have had him as a father and so proud to be his son. My hope is that his contributions to the entertainment industry will be remembered for many years to come."

With his wife Eydie Gorme, Steve was part of one of the country's most beloved singing duos way back in the day ... Steve and Eydie got their start in the 1950s and performed together until 2009, when she retired.

Steve and Eydie sang on lots of variety and late-night shows, including "The Judy Garland Show," "The Julie Andrews Hour," "Night Gallery," "The Danny Kaye Show," 'The Tonight Show,' and lots of others.

He and his wife also played Las Vegas nightclubs -- and in the 1980s ... they played sold-out shows at Carnegie Hall as well. Steve even opened for Ol' Blue Eyes during his 'Diamond Jubilee' tour ... so yeah, he used to roll with the best of them in those days.

Steve's biggest hit song from his solo career ... his 1962 single, "Go Away, Little Girl," which hit No. 1 on the charts.

As an actor, Steve earned a Tony nomination for his work in the Broadway musical "What Makes Sammy Run?" He also starred alongside Eydie in another musical, "Golden Rainbow."

Steve won a Primetime Emmy for a TV special celebrating Irving Berlin, and he had a bunch of other TV credits, on shows like "The Nanny" and "Hot in Cleveland."

Lawrence was 88.