The cult star, who had battled drug and weight issues for years, suffered a fatal heart attack while in rehab in 1995, just eight days before his 53rd birthday.
The group officially disbanded following Garcia's sudden death, although the surviving members of the jam band have since toured with various different line-ups.
However, Lesh insists Garcia's tragic end continues to haunt him.
He tells Rolling Stone magazine, "It's taken me 15 years to come to terms with Jerry's death. And I'm not completely there yet."