Alright, I finally ended up figuring this out on my own. The issue was you have to create a light object, and for some reason when I called camlight it didn't work on the axes I was interested in, so the gouraud lighting didn't take effect. I had to experiment to find out how to do all of the proper syntax when specifying the axes, but here's my solution for anyone who may run into this issue when using App Designer:
trisurf(tri, outXYZ(:,1), outXYZ(:,2), outXYZ(:,3),'FaceColor','yellow','EdgeColor',...
'none','FaceAlpha',1, 'Parent', app.KneeMask);
daspect(app.KneeMask, aspect_view);
camlight(app.KneeMask);
lighting gouraud;
view(app.KneeMask,3)
axis(app.KneeMask, 'tight');