I think the biggest tip I could give is to always be working on something. Completely immerse yourself in whatever you're doing. If you think of something, write it down. Creativity wont come when you sit down and stare at a piece of paper and wish, it's spontaneous. Wherever you are, be it your desk pencil in hand, or in the car on your way to work, when that moment hits you have to milk it for all its worth. Even if its just scattered thoughts, that's better than nothing. Just looking at a few words from the past can spark a thought enough to coddle into a master piece. The hardest part is always getting started, so start. You may be shitty at first but that's more than 90% of the population can say. Even the greats where beginners at one point.

On a side note. If you're looking to produce your own music as well as write it (which you probably will at first) you should download a DAW. While lyrics can be written pretty much anywhere recording is a bit more difficult. You can always use your phone but if you have a computer I would highly recommend downloading Reaper or Audacity. Audacity is pretty limited but it is free. Reaper is a full-fledged DAW capable of pretty much anything you can do in a studio. While Reaper isn't technically "free" the license is super cheap for a DAW ($60?) and I don't believe you even need a licence to use it.

"Without melody there can be no lyrics"

I disagree. Lyrics are simply words. Whether they are set to music or not has nothing to do with their classification as lyrics. Of course all music has a melody and most lyrics follow some sort of meter, but the melody doesn't make the lyrics, nor do the lyrics make the melody. I'd be willing to bet that the majority of spoken word had lyrics written before a melody. A prime example would be La Dispute's "Here, Hear". Each of the tracks from the first two EPs are actually based off of previous works of literature. Are they still lyrics? Yes. Where they created for the music? No, quite the opposite actually. With or without a melody, lyrics are just poetry.

Really, what you write first all comes down to what the focus of the song is. If you're writing something centered around lyrics then lyrics will probably be top priority. If you're writing some twisting crazy math rock then lyrics are probably second in line. I don't think the point is to create lyrics for a song, or the other way around, but rather build off of what you've already created. Write lyrics and when you find a melody that fits, use it. Write melodies and when you think of words that fit, use them. As someone else said, keep the momentum going.