Both men are definitely grappling-based fighters, but both men have also developed their striking along the way.
Jim Miller has won three of his 21 wins via knockout, which is a low percentage. His striking is usually a tool to set up takedowns for himself, but he has earned a knockout from knees and punches in the UFC over Kamal Shalorus.
Joe Lauzon may have some of the most underrated boxing in the UFC, due mostly to his dangerous submission game. He's won four of his 22 victories by knockout, including UFC KOs of Kyle Bradley and Jens Pulver.
Don't forget that it was Lauzon's striking that dazed Melvin Guillard in under a minute, allowing him to choke out the feared lightweight.