Hey Glenn, interesting post on where to find inspiration to write! Also good to read how Shi, Ann and Kells and Ruth find the words. My two cents.
First, the mechanics. I jot down ideas in my cellphone and iPad for emailing to myself for download onto a main iMac for polishing and matching with downloaded jams. These then get recorded, mastered and uploaded (well, the good ones do :) ).
Inspiration... I find it's a bit like love - it's all around but you only feel it when it hits you. It is a sense that I believe can be developed - an openness for the mind to recognise and catch ideas as they float past the brain. A sense of "whoa... That might make for a song." An attitude of Idea mindfulness, perhaps.
Much of mine comes from people watching and people listening. Wondering how is this persons life and how it is significant and how is it different and worth writing about. And what they say and how and why they say it often make for titles which can be expanded upon. I also look for the bizarre, the absurd and the ridiculous and look to expose and Spotlight the thing through shining a lyrical light.
Creating and imagining a character also works. As Singers, we are the storyteller of the song and need to act out that story. As the writer, we need to lyrically express what and why the character feels the way they do. Empathising and walking their walk can generate good lines. Though it is good to create a context and so avoid the thing becoming too self exploring and a bit me me me... Received wisdom is that listeners don't really care about you - they care about THEM and how they relate to the song and its character. Thinking about how a listener hears the song can be good for adjusting words, but that is a whole other ballpark. Most songs look to provoke an emotional response in a listener; keeping this in mind can lead to sharper word selection and precision in that response.
Like Shi, Anne and Kells, I find the titles of the jams on Wikiloops are good sources of inspiration for lyrics. Many of mine have come from something sparked by titles given by the members. Sometimes the generated lyric fits the jam of the title, sometimes not. Those occasions I have tried to write for a specific title and jam have produced mixed results. Some sparkle, some are still stuttering and unfinished. Old song titles can be reworked (my research says titles can't be copyrighted, only lyrics) or reimagined. How about Honky Tonk Women becoming Honky Tonk Men? :o
I usually write my lyrics in metre and rhyme, though ideas are often in prose until such time as the mind comes into season to lyricise them. I just find the challenge and discipline of writing in rhyme hugely satisfying.
My mainstream is rock and blues, and I often proceed from the position that everything is blues. Tack a word or phrase in front of "Blues" and I am usually off on the hunt. I am the Blues Hunter. Hunting Blues. See what I mean? ;)
One of the better traditional sources for ideas is anger. And passion. What makes you angry and why? What do you have a passion for? Words flow easier when you have something really driving you. Though some ideas do take longer than others to develop. I have ideas dating back years that still won't seem to evolve. Whilst others are finished in minutes. So it goes. All things in their time. Love is the traditional inspiration for lyrics. Not one of my main sources at this time. So it goes.
In terms of fitting lyrics to the jams, I find it works to be flexible. If the jam arrangement works, then I will adjust the lyric to fit. If not then I either find a different jam or cut and paste the jam to fit my envisaged (usually standard song formula) arrangement. Perhaps not what the music Composer might have had in mind (and some can be very insistent not to screw with their arrangements) but I feel a need for some give and take for the sake of a completed song. It's only a song, after all.
In terms of matching, the tone of both the jam and the lyric are the critical factors. Rock for angry and attitude, Blues for sad and gospel/spirit, jazz and funk for fun, world and folk for causes, reggae for... Reggae. My lyric writing seems to span a wide range of tones and styles, and I normally add a descriptor in the title when the lyric feels finished. Kind of what style and genres I feel the lyric might fit. Then when I have a jam playing I can scroll through the lyrics and audition them for tryout and consequent selection for recording. Quite often, a lyric tagged for one genre will, with some tweaking, surprisingly fit in another. Keeping open to possibilities seems to be the key. Beware the mental straitjacket!
In terms of not being able to generate a lyric, in my time I have found best not to fret too much about feeling non productive. Writers Block is real and it happens. For my block periods (which seemed to correspond with massively blue periods) I tried to write about it. Just verbal diarrhoea on the screen, let it all out, scream, swear, rant, curse, whatever it takes. No one need see it but you and I found the catharsis of doing this kept the idea of writing alive. And these bouts occasionally got followed with something in writing I felt to be worthy.
The thing to remember is that the writing will come back. The block is a cloud in front of the sun, but the sun is always there. Just keep open to life and what it gifts to you during the dry times. I have been amazingly lucky in that somehow lots of the memories and experiences got retained and they somehow surface when they need to, to underpin a lyric. If you need to write, and you know you need to write, you will write in your time. The imagination will make sure of it.
Phoooo... Big two cents. Hope it helps. Keep writing!