They never really played against each other at their peaks.
Lombardi coached from 1959 to 1969, and his last great team was the 1967 Packers. He retired for a year, then coached the Redskins in 1969 before dying of cancer.
Shula started coaching in 1963 and really hit his stride shortly after Lombardi retired. They met once in the playoffs, Lombardi won. Shula was coaching the Colts.
Fun note: Shula actually built two Super Bowl teams. He built the Baltimore Colts, but when the Colts lost to the Jets in the Super Bowl, he went to Miami. Don McAfferty won the Super Bowl the next year with Shula's players, but the team fell apart. It was similar to Switzer winning a Super Bowl with Jimmy Johnson's players, Shula vs Chuck Noll was interesting, but Shula's Dolphins got good right before the World Football League started, and he lost a lot of key players to them. Noll's Steelers got good right after the WFL collapsed, so he was able to maintain his players, creating the 1970s dynasty.
Shula brought a lot of ex-Colt players over to the Dolphins, notably Earl Morrall, who many forget, took over for Greise in 72 after he got hurt, and kept the Dolphins perfect, until Greise returned for the Super Bowl.
It was crazy that in 1972, the Dolphins, even with their perfect record, still had to play the AFC Championship Game, in Pittsburgh.
“Shula was coaching the Colts”
Please say the “Baltimore Colts.” That’s when the Colts were the Colts!