D'Amour's plays have included Hide Town produced by Infernal Bridegroom Productions, Houston (2006), Anna Bella Eema Produced by New Georges, NYC (2003), Blue Theater/Physical Plant, Austin, TX (2001), Ten Thousand Things, Minneapolis. Winner, Best New Play, Austin Critics’ Table (2002), the Obie Award–winning play Nita and Zita Produced by HERE, NYC 2003 and ArtSpot Productions, New Orleans, 2002, The Cataract at the Women's Project in New York (originally produced by PlayLabs, Minneapolis, MN, 2003 and then in Providence, Rhode Island by Perishable Theatre). Also, Stanley 2006 was to go up at HERE Arts Center in SoHo, NYC but was withdrawn due to an intellectual property dispute involving the character Stanley Kowalski. In August 2008, she collaborated with the printmaker / installation artist SWOON on Swimming Cities of Switchback Sea, a fleet of seven intricately handcrafted vessels that navigated the Hudson River in August 2008. Lisa made a performance to be presented by the crew in towns along the Hudson. Detroit, set to première on Broadway in 2011, coming off the production at the Steppenwolf Theatre Company, directed by Austin Pendleton. Instead, the play will open the 2012-13 season at Playwrights Horizons.
- 2002: Best New Play from Austin Critics’ Table for Ten Thousand Things
- 2003 Obie Award for Nita and Zita
- 2008: A grant from the Alpert Awards in the Arts in Theatre, a $75,000 mid-career grant
- 2008: 'MAP' fund award for Terrible Things with collaborator Katie Pearl
- 2011: Steinberg Playwright Award  with Melissa James Gibson.