The bassist achieved international success with the group during the 60s and 70s with hits including Rockin’ All Over The World and Whatever You Want.
Status Quo singer Francis Rossi labelled Lancaster as an “integral” part of their sound as he paid tribute to the musician.
Lancaster, who was born in Peckham, south London, in 1949, last toured with the band in 2014.
The musician, who had reportedly been living in Australia, also performed with bands The Bombers and The Party Boys.
Rossi said in a statement: “I am so sorry to hear of Alan’s passing.
“We were friends and colleagues for many years and achieved fantastic success together as the Frantic Four alongside Rick Parfitt and John Coghlan.
“Alan was an integral part of the sound and the enormous success of Status Quo during the 60s and 70s.
“Although it is well documented that we were estranged in recent years, I will always have very fond memories of our early days together and my condolences go to Dayle and Alan’s family.”
Rossi and Lancaster first began performing together in the 1960s under a number of different band names before settling on Status Quo.
The group went on to have four UK number one albums, according to the Official Charts Company.
Status Quo manager Simon Porter said: “This is such sad news and my sincere condolences go out to Dayle and the family.
“It was an absolute pleasure to be able to reunite the original line-up for two sell-out tours in 2013/2014 and to give Status Quo Frantic Four fans a final legacy and such a lasting memory.
“Although Alan was not in the best of health even then, he got through the tours with determination and grit and was a pleasure to work with.”