You can simply tape your mouth shut with Zippit Mouth Tape even if you have dry lips. By not breathing through your mouth anymore you strengthen your oral health which will also make you less likely to suffer from dry lips.  The adhesive of the strip sticks well enough to hold your lips together but is not so strong that it harms your lips. Tip: Remove the strip by pushing the strip out from the inside with your tongue. This allows you to remove the strip from your lips completely painlessly, and without leaving any tears.