To better understand the experiences of the homeless community near Lydia's office, she visited the homeless shelter over the course of a month and spoke with the people who stayed there nightly. What type of research method did Lydia use?

ethnography

Explanation:

Ethnography -

It refers to as a quantitative and qualitative research method, for studying certain specific group or society.

The method require to have a proper search and information for the subject.

The example are some groups like communities, organization, etc.

Hence, from the given scenario of the question,

The correct answer is ethnography.