The Patakara Lip Trainer see http://tinyurl.com/q65npyg is a lip exerciser with a benefit for asthma sufferers, see web page " weak lip closing strength causes oral breathing while sleeping and is also one of the reasons that cause asthma attacks." Then the text goes on to say "People who suffer from asthma, please note whether or not you nasal breathe while sleeping. If you do (not) nasal breathe, please be sure to use Patakara immediately."
For another lip trainer (with detailed illustrations) see http://tinyurl.com/m4fhv94 See an excellent informative video for the device on https://www.youtube.com/watch?v=vSi0TkKWgOg
But it seems that all grownups and kids need for the exercises is a pacifier, see witty but helpful video https://www.youtube.com/watch?v=oQxNoI2ACu0 . You keep at it till the lip muscles tire.
See also http://www.lsfo.co.uk/mouth-breathing-and-asthma/ as a cause of asthma "We speculate that asthmatics may have an increased tendency to switch to oral breathing, a factor that may contribute to the pathogenesis of their asthma."