Lach was the recipient of the first official Art Ross Trophy in 1948 and the Hart Trophy in 1945. He did lead the NHL in scoring during the 1944–45 season with 80 points, but this was before the creation of the Art Ross Trophy. Elmer was the centre of the great "Punch line" with Toe Blake and Maurice Richard. He was inducted into the Hockey Hall of Fame in 1966.
Elmer won the Stanley Cup three times in the years 1944, 1946, and 1953.
In 1998, he was ranked number 68 on The Hockey News' list of the 100 Greatest Hockey Players.
| Regular Season | Playoffs | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Season | Team | League | GP | G | A | Pts | PIM | GP | G | A | Pts | PIM | ||
| 1940–41 | Montreal Canadiens | NHL | 43 | 7 | 14 | 21 | 16 | 3 | 1 | 0 | 1 | 0 | ||
| 1941–42 | Montreal Canadiens | NHL | 1 | 0 | 1 | 1 | 0 | -- | -- | -- | -- | -- | ||
| 1942–43 | Montreal Canadiens | NHL | 45 | 18 | 40 | 58 | 14 | 5 | 2 | 4 | 6 | 6 | ||
| 1943–44 | Montreal Canadiens | NHL | 48 | 24 | 48 | 72 | 23 | 9 | 2 | 11 | 13 | 4 | ||
| 1944–45 | Montreal Canadiens | NHL | 50 | 26 | 54 | 80 | 37 | 6 | 4 | 4 | 8 | 2 | ||
| 1945–46 | Montreal Canadiens | NHL | 50 | 13 | 34 | 47 | 34 | 9 | 5 | 12 | 17 | 4 | ||
| 1946–47 | Montreal Canadiens | NHL | 31 | 14 | 16 | 30 | 22 | -- | -- | -- | -- | -- | ||
| 1947–48 | Montreal Canadiens | NHL | 60 | 30 | 31 | 61 | 72 | -- | -- | -- | -- | -- | ||
| 1948–49 | Montreal Canadiens | NHL | 36 | 11 | 18 | 29 | 59 | 1 | 0 | 0 | 0 | 4 | ||
| 1949–50 | Montreal Canadiens | NHL | 64 | 15 | 33 | 48 | 33 | 5 | 1 | 2 | 3 | 4 | ||
| 1950–51 | Montreal Canadiens | NHL | 65 | 21 | 24 | 45 | 48 | 11 | 2 | 2 | 4 | 2 | ||
| 1951–52 | Montreal Canadiens | NHL | 70 | 15 | 50 | 65 | 36 | 11 | 1 | 2 | 3 | 4 | ||
| 1952–53 | Montreal Canadiens | NHL | 53 | 16 | 25 | 41 | 56 | 12 | 1 | 6 | 7 | 6 | ||
| 1953–54 | Montreal Canadiens | NHL | 48 | 5 | 20 | 25 | 28 | 4 | 0 | 2 | 2 | 0 | ||
| NHL Totals | 664 | 215 | 408 | 623 | 478 | 76 | 19 | 45 | 64 | 36 | ||||