If the owner installs an app can a secondary profile use it? It appears that in Lollipop secondary user profiles can no longer install APKs from unknown sources.

So, if I install an APK from the owner profile, can I give a secondary profile access to that app?

Suggested tag: secondary-profile
Yes, as long as the user is a Restricted User.  When you first create the user, you must choose "Restricted User".  Then you can choose what apps the user can access (4.2 style).