The France captain was at fault for dropping a simple cross into the box before falling backwards as Neal Maupay headed into an empty net to give Brighton a dream start after just three minutes.
Lloris was given oxygen as he was carried from the field, seemingly nursing an elbow injury, and will now be a major doubt for upcoming Euro 2020 qualifiers against Iceland and Turkey.
The early goal was a blow to Tottenham's confidence as they attempted to bounce back from a 7-2 thrashing against Bayern Munich in the Champions League on Tuesday.