Lyrics first, then chords, then melody is a fairly standard way for songwriters who write both lyric and melody for their songs. It works but, as mrx suggested, it has some drawbacks.
Some of the great composers of the past developed a procedure that often resulted in wonderful music. They began with the title and a general idea of what the song was about. No words or music were considered until a memorable and singable title was established. Knowing the title beforehand let them consider title placement inside the verse or chorus (depending on the song's structure). Next the chords and melody were developed (before the lyrics). Title placement, singable melody notes, repeating melodic phrases, etc. were all considered without the restrictions of a pre-existing lryic. Better and more creative melodies were often the result. The lyric was then written to fit the existing melody. Obviously, this process made lyric writing much harder; but the resulting lyrics were rhythmically stronger and tighter and more singable.
Give it a try. You might be pleasantly suprised at the results.
Keep writing,
Don