Your instrument is often a source of inspiration for new songs. Try new tunings on guitar, or alternate chord inversions on keyboard. Sometimes a change in sound will move you in new directions. A different patch or changing from acoustic to electric guitar can produce novel colors and spawn ideas. Try playing chords or patterns that you think of as "wrong" to create progressions that aren't obvious. You can even try playing a new instrument.
Keeping a notebook to capture possible song titles or catchy phrases is one way to create a source of ideas when the writing mood hits without new inspiration. Creating outrageous metaphors can jump start unique writing. Make a list of 25 adjectives and a separate list of 25 nouns. Combine them arbitrarily. "Curious Brick" might not make its way into your song, but the exercise will likely change the way you look at creative description.
Often, words suggest melodies and melodies suggest words. Try humming your lyric without an instrument, then playing chords to support the melody. Starting from a chord or melody, you can fit vowel sounds that might suggest sentences when strung together. Using "filler" words is a common practice to fix a melody in memory until your final lyric comes along. The Beatles' "Yesterday" started life as "Scrambled Egg."
Existing songs can serve as inspiration for new material. You can write different words to a favorite song, then later create a new melody and chords for the lyric you write. Working the other way, try using a poem or song lyric that is already written and devise new music for it. When you have a hot new track, then approach it for original lyrics.