The French international stopper moved to White Hart Lane in the summer, but has vied with the veteran Brad Friedel to be first-choice in Andre Villas-Boas' side.
Five of Lloris' 13 appearances so far have come in Spurs' successful bid to make the knock-out stages of the Europa League.
"Drawing Tottenham, it made us all think about Hugo," admitted former Arsenal defender Garde.
"That is fate. It will probably be quite moving for him here. I hope he will not want to shine against us, but I fear he will."
The draw also made Garde recall his three-year stint with Spurs' North London rivals Arsenal in the latter half of the 1990s.
"White Hart Lane? It won't be too difficult to remember. Of course there are memories that come back," he said.
"I am not sure if the Spurs' fans will remember my period with Gunners, but maybe that night they will make an effort."