Not feeling so inspired? Well go ahead and write anyway. After all, inspiration is only a fraction of the ingredients for brilliant songwriting; the rest is made of dedication and hard work. Build your work ethic up by writing song lyrics even when nothing comes to mind. Just write down anything no matter how bad the lyric may be. Don't worry about spending time editing; nobody is going to read it but you.
Listening to your favorite music can put you in the mood to write songs of your own. Start each morning by playing some old favorites, followed by something you haven't heard before. New music often pushes creativity within the songwriter like an inspiration domino effect.
If you're having trouble getting into the groove of things, then perhaps you should try doing something else for a while. It sounds counterintuitive, but an activity such as going for a walk, exercising or playing video games before tackling songwriting might help ease the mind and prepare it to write.
It's a good idea to log your daily activities in a journal to get ideas for lyrics. Random moments in your everyday life may very well sync up in a significant way, creating a brand new song for you to put under your belt. Carry the journal with you wherever you go and keep track of ideas that strike randomly throughout the day.