Emily was upset about the way House was treating Dominika, specifically how he openly slept with her with Dominika in the living room. She wanted to stop the business relationship without hurting his feelings. As such, she made up a story that she was leaving the business and showed House a picture of her together with Harris, representing him as her fiance.
However, House wouldn't let the matter rest. He convinced himself that, since Harris was okay with Emily's past as a prostitute, he probably had skeletons in his own closet. As such, he worked on a plan with Dominika where she would try to seduce Harris to show Emily that he would not be faithful in their relationship.
When the duo found out where Harris worked, Dominika approached him and asked him to have sex with her. He immediately agreed, only to be confronted by House. However, after a few seconds of confusion, Harris told House he knew Emily because she was his sister. House realized he had been tricked and that Harris's willingness to sleep with Dominika was merely a normal reaction to opportunity.