The 26-year-old joined the London club from Lyon last summer and has now established himself as the first-choice goalkeeper in Andre Villas-Boas's team.
This is the first time in his career that Lloris has had no break from football over the Christmas and New Year period, as he had in France when he was with Nice and Lyon.
However, the Frenchman insists that he has adapted to life in England and is enjoying the experience.
"Mentally you have to make an effort during the festive period," Lloris told L'Equipe. "There will be a few days' rest after the Cup matches in January to get back freshness.
"But I have fun every day. I am here to improve and push the limits in a different culture. It is important on a sporting level, but on a human level too.
"I am still discovering the English stadiums, the perfect pitches and the atmosphere. I have great fun."