Over the next decade, the bassist found himself an in-demand live and session player, recording albums with artists such as Frank Foster, Chet Baker, John McNeil, Warne Marsh, and Kirk Lightsey, to name a few. Also during the '80s, he was a member of the Radiojazzgruppen, Ernie Wilkins' big band, Thad Jones' big band, and the DR Big Band. He also performed regularly with Doug and Jimmy Raney, Paul Bley, and Duke Jordan. As a leader, Lundgaard made his recording debut in 1994 with This Bass Was Made for Walking. He followed it up with co-lead sessions like 1995's Playing in the Breeze alongside trumpeter Thomas Fryland and guitarist Jacob Fischer, and 1999's Fine Together, with Fischer and saxophonist Anders Lindskog. Lundgaard also formed the Repertory Quartet with saxophonist Bob Rockwell, issuing a number of albums like 1995's Turn Out the Stars: The Music of Bill Evans, 1996's Plays Ellington/Strayhorn, and 1998's Plays Mingus/Pettiford.
Away from performing, Lundgaard stayed active teaching and holding master classes in various conservatories in Denmark, Rotterdam, Zürich, and Helsinki. In 2002, he joined drummer Alex Riel and pianist Kenny Werner for Celebration (an album marking Riel's 60th birthday), and then followed up with albums with Svend Asmussen, Jan Lundgren, and Thomas Claussen. He joined fellow bassist Mads Vinding for 2005's Two Basses, and led his own trio for 2007's Plays Cornelis. Lundgaard then backed tenor player Scott Hamilton for 2011's Scott Hamilton Meets Jesper Thilo, as well as for the saxophonist's 2013 outing Swedish Ballads & More with Jan Lundgren. In 2015, Lundgaard issued the trio date 60 Out of Shape, featuring pianist Enrico Pieranunzi and drummer Riel. ~ Matt Collar