The hospital said the case was confirmed on Monday.
According to Houston Methodist, as of Monday, July 19, there are 185 patients diagnosed with COVID-19. The hospital said the majority of them are unvaccinated.
About 85% of those patients have been diagnosed with the Delta variant, which is reportedly more contagious.
The WHO said the Lambda variant was first detected in Peru in August 2020.
"We're seeing an alarming spike in the number of COVID-19 cases across the Houston area, with the steepest increase happening over the weekend," said Houston Methodist in a statement. "The increased hospitalizations add stress to many of our hospitals that are nearing capacity."
The hospital system is encouraging vaccinations.