Lancaster had several international hits with the group during the 60s and 70s including Rockin' All Over The World and Whatever You Want.
Manager Simon Porter said: "This is such sad news."
Lead singer Francis Rossi said: "Alan was an integral part of the sound and the enormous success of Status Quo during the 60s and 70s."
Rossi and Lancaster 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.
He said in a statement: "We were friends and colleagues for many years and achieved fantastic success together as the Frantic Four alongside Rick Parfitt and John Coghlan.
"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."
Mr Porter gave his "sincere condolences" to Lancaster's wife Dayle and the family.
"It was an absolute pleasure to be able to reunite the original line-up for two sell-out tours in 2013-14 and to give Status Quo Frantic Four fans a final legacy and such a lasting memory," he said.
"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."