Sharron Singer, 47, suffered "significant" injuries to her arms and legs after she was bitten on Tuesday morning in Wrangle, near Boston.
The Communication Workers Union (CWU) said her life had been "in danger" and urged owners to be responsible.
Lincolnshire Police said the dog had been seized and put in a kennel.
More on this and other stories across Lincolnshire
Mrs Singer, who remains in hospital, needed four hours of reconstruction surgery and skin grafts to repair muscles, tendons, nerves and ligament damage to her arm, the CWU said.
The CWU said: "Sharron's life was in danger when this attack took place and we are just relieved that she survived. Her life however will never be quite the same.
"I only hope the physical and psychological damage sustained in this attack can be repaired, but it won't be 100%."
A union spokesperson said the dog was "of a powerful, athletic breed".
Lincolnshire Police is investigating but said no arrests have been made. It could not confirm the breed of dog that was seized.
Royal Mail said the safety and welfare of its staff was "paramount" and confirmed deliveries to the house had been suspended.
Morag Turnbull, spokesperson for Royal Mail, said: "Our thoughts are with her and her family at this distressing time.
Both Royal Mail and the union appealed for "all dog owners to be more responsible and to control and restrain" their pets during deliveries.

Damien Reeves broke the deadlock by finishing via the crossbar from James Lawrie's cross before Josh Ginnelley doubled the lead after a 50-yard run.
Jake Moult ended the game as a contest, converting a penalty after the lively Lawrie was fouled by Omar Beckles.
And Jordan Sinnott completed the Shots' miserable afternoon, scoring after good work from Ginnelly.
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Aldershot Town boss Barry Smith told BBC Surrey: "We didn't defend properly and their front four caused us so many problems.
"It was down to us not defending properly for the first goal. It comes from a centre-back not being dominate and we couldn't get a grip in the game.
"We lost battles all over the park today. Once you cross that white line it is down to the players to make sure they are doing the jobs that they've been asked."
The Royal Mail and a union representing postal workers have urged dog owners to "control and restrain" their pets after a postwoman was attacked.
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Altrincham moved out of the National League relegation zone with an impressive victory over Aldershot.