Same process, more or less. I'll record the progression on guitar and/or bass and then set the DAW to loop over it. Then I will stand in front of the mic and make an absolute fool of myself, humming, screeching, singing scat, whatever, the point being to find a melody that works. If nothing works, I'll abandon the song. If something does, then I'll go through those takes and comp together the best bits. Somewhere in that process, words and phrases will have appeared miraculously. Not complete lyrics, but key parts. If not, I abandon the song and move on, returning to it maybe later, maybe never. Then comes the hard part: finishing it. To do that I need to ask myself what the lyric is going to be about: perspective, situation, mood, story line, etc. With a melody and a theme, I can finish it, but it may take a long time. The melody may evolve as the lyrics develop. When I have finished lyrics, the song is done.
It helps to avoid getting too invested in unfinished songs. I'm always working on many songs at once. Like most songwriters, I've got dozens, maybe hundreds in various stages of completion. Some of those will be finished, most never will. Some may become a chorus, verse or bridge for some other song. Only when a song is pretty close to finished will I give it my undivided attention.
If you want to try this method, set aside a few hours a week to jam on your preferred instrument, preferably over a drum loop. Have your studio set up already so that you can record the promising parts, and set up a file system where you can find them easily later. My unfinished songs are titled as a date: 4_19_2016, and they are saved in a folder with the same title within a directory called Unfinished_2016, which in turn sits in a directory with folders of unfinished tracks from years gone by. Any particularly promising hooks in the song will get rendered to audio and saved the same folder, so I can give them a quick listen at a later date.