Ronald James Chadwick, 39, of Portland Terrace, and Leanne Kay Housham, 21, of Clinton Terrace, both appeared before Lincoln Magistrates on Monday 9th July.
They admitted charges of causing unnecessary suffering to their pet cat, named Mario, over a two week period between November and December 2011.
The court heard how the pair, who were living together as a couple, failed to take Mario to a vet when he broke a leg.
His injuries were found to be so bad that he was put down.
Defending, Mr Lloyd Edwards said the couple had owned two cats, Mario and Fifi, and that Fifi was in good health.
Mario, however, had sustained a broken leg by trapping it in a stair gate.
“My clients took Mario to the vet,” said Mr Edwards.
“But at this time they were both on benefits and had financial problems, children to look after, and they could not pay the vet fees.”
Mr Edwards explained how help from the RSPCA and the Cat Protection League (CPL) enabled them to afford treatment and an amputation for Mario.
But in November 2011 a social worker noticed that Mario - now a three-legged cat - seemed to have another leg injury.
“He had been eating properly and had not lost any weight, so my clients did not realise how seriously hurt he was,” said Mr Edwards.
“But they did know they could not afford any vets fees, after seeing how much it had cost last time.”
The court heard that they were refused any more help from the CPL, and without the means to pay a vet, they hoped the problem would simply resolve itself.
Mr Edwards said: “In hindsight they wish they had been more forceful with the CPL and realised the cat was in much more pain than they thought.”
“If they are to have animals in the future they now know the importance of pet insurance.”
The chair or the bench said it had been a ‘case of neglect’, banning Chadwick and Housham from having any animal for three years.
Chadwick, a fishmonger, must pay £250 in fines and costs. And Housham, who is unemployed, must pay £100.