Frank genuinely smiling because of Karen.
Allura pilots the Black Lion and gets annoyed when she finds out Black is hiding something from her. It's even worse when she finds out about Shiro. After some arguing with her, the Lion lets her see it. It's over an hour later when the others come looking for her. She's red faced and flustered. Black was hiding treasured memories of Shiro gushing about 'this most beautiful princess' to her.