The French No. 1 moved to White Hart Lane from Olympique Lyonnais in the summer and, although he did not walk straight into the starting line-up due to Brad Friedel's form, the 26-year-old is now Andre Villas-Boas' established first choice.
Spurs have enjoyed a successful December and January, losing just once from six league games so far, with Lloris playing in each match and conceding just twice.
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"Mentally you have to make an effort during the festive period," he told L'Equipe. "There will be a few days' rest after the cup matches in January to get back [to] 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."
Spurs' 3-1 win over relegation candidates Reading on Tuesday sees them climb above Chelsea into third position in the table, but the Blues can jump back ahead when they face QPR on Wednesday evening.
The result also puts Villas-Boas' side five points in front of local rivals Arsenal, who lost ground by drawing 1-1 with Southampton.
Next up for the Lilywhites, as the busy schedule continues, is a break from league duties as they welcome Coventry to White Hart Lane in the FA Cup on Saturday.