Our list of reasons for writing lyrics began with several different situations in which you actually have something you want to say. When you have something to say, you don’t need to have music first. What you want to say will be the initial constraint that guides your writing, rather than listening for parts of the melody that “sound like they’re saying something.”
A lyricist should be prepared, therefore, for inspiration to strike. I prefer to write lyrics by hand, and thus think that notebooks are one of the greatest things ever. But a nice thing about writing lyrics on a computer is that you can make changes much more easily. Well, you can also type faster than you can write, so that can be helpful too if you need to “get it all written down” quickly.
And nowadays—as opposed to when I first started writing back in the 90s—most people have some sort of computer (even if it’s just their phone) within reach at most times.
The point is that whichever method you prefer, you’ll need to have that method available to you when you get an idea for a set of lyrics, and you’ll need to be ready to make changes as you go (even if that means rewriting the lyrics by hand).