I’ll have to find my specimen, but McCune and Geiser (2009) have a page on L. rivals, and say “lobes…rounded apices 0.2-1.0(1.5) mm broad”.
also “Most observers in the upright (standing) position will overlook the dark, tightly appressed rosettes…Look for it on rocks in and along clear cold streams in the mountains. L. rivals varies considerably in form, suggesting that it may include more than one species or that it shows great environmental plasticity.”
It is found along with Peltigera hydrothyria in Opal Creek, OR.
also see Glavich 2009 Distribution, rarity and habitats of three aquatic lichens… in The Bryologist 112(1);54-72